# Geometry - Pythagoras Theorem

**Question 1**

__The hypotenuse is the side opposite the right angle__Which letter represents the hypotenuse in these triangles?

a)

a
s

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**Question 2**

__The square of the hypotenuse is equal to the sum of the squares of the other two sides__Find the area of the shaded square

a)

a
$25$cm$^2$

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b)

a
$169$mm$^2$

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c)

a
$9$m$^2$

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d)

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$36$cm$^2$

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e)

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$16$m$^2$

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f)

a
$1$m$^2$

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**Question 3**

$a^2+b^2=c^2$

Find the value of $x$

a)

a
$x=5$cm

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b)

a
$x=10$cm

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c)

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$x=13$cm

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d)

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$x=15$cm

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e)

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$x=17$cm

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f)

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$x=41$cm

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**Question 4**

Find the value of $x$. Leave your answer as a square root

a)

a
$x=\sqrt{13}$cm

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b)

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$x=\sqrt{65}$mm

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c)

a
$x=\sqrt2$m

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d)

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$x=\sqrt{97}$cm

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e)

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$x=\sqrt{149}$m

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f)

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$x=\sqrt{277}$mm

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**Question 5**

Find the value of $x$. Calculator recommended

a)

a
$x=45$cm

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b)

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$x=65$cm

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c)

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$x=53$mm

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d)

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$x=65$m

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e)

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$x=109$cm

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f)

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$x=145$m

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**Question 6**

Find the value of $x$. Calculator needed. Leave your answer rounded to one decimal place.

a)

a
$x=5.8$cm

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b)

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$x=8.6$inches

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c)

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$x=12.5$m

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d)

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$x=15.6$cm

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$x=27.7$mm

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$x=34.7$cm

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**Question 7**

Find the value of $x$ by finding Pythagorean Triples/Triads. No calculator

a)

a
$x=50$cm

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b)

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$x=0.5$cm

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c)

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$x=0.1$m

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d)

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$x=\frac57$cm

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e)

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$x=1300$m or $x=1.3$km

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f)

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$x=3.4$mm

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**Question 8**

Find the value of $x$. Calculator needed. Leave your answer rounded to two decimal places.

a)

a
$x=5.02$cm

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b)

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$x=0.44$m

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c)

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$x=10.47$m

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d)

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$x=14.26$mm

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$x=2.63$km

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f)

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$x=7.77$m

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**Question 9**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. No calculator

a) $3,4,x$

a
$x=5$

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b) $5,12,x$

a
$x=13$

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c) $8,15,x$

a
$x=17$

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d) $0.05,0.12,x$

a
$x=0.13$

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e) $8\,000,15\,000,x$

a
$x=17\,000$

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f) $15,20,x$

a
$x=25$

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g) $\frac{5}{23},\frac{12}{23},x$

a
$x=\frac{13}{23}$

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h) $\frac34,1,x$

a
$x=\frac54$ or $x=1\frac14$

Question ID: 30030080080

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i) $9,40,x$

a
$x=41$

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j) $88,165,x$

a
$x=187$

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k) $\frac25,\frac34,x$

a
$x=\frac{17}{20}$

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$\frac25,\frac34,x=\frac{8}{20},\frac{15}{20},\frac{20x}{20}$

$8$ and $15$ are in a Pythagorean Triple with $17$

so $20x=17$

$x=\frac{17}{20}$

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l) $\frac32,\frac{36}{7},x$

a
$x=\frac{75}{14}$

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$\begin{align}\frac32,\frac{36}{7},x&=\frac{21}{14},\frac{72}{14},\frac{14x}{14}\\&=7\times\frac{3}{14},24\times\frac{3}{14},4\frac23x\times\frac{3}{14}\end{align}$

$7$ and $24$ are in a Pythagorean Triple with $25$

$\begin{align}4\frac23x&=25\\x&=25\div\frac{14}{3}\\&=25\times\frac{3}{14}\\x&=\frac{75}{14}\end{align}$

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**Question 10**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Leave your answer as a square root

a) $6,11,x$

a
$x=\sqrt{157}$

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b) $9,20,x$

a
$x=\sqrt{481}$

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c) $12,13,x$

a
$x=\sqrt{313}$

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d) $1,5,x$

a
$x=\sqrt{26}$

Question ID: 30030090040

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e) $1,1,x$

a
$x=\sqrt2$

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f) $13,14,x$

a
$x=\sqrt{185}$

Question ID: 30030090060

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**Question 11**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Calculator required. Round your answer to three significant figures

a) $4,7,x$

a
$x=8.06$

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b) $8,8,x$

a
$x=11.3$

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c) $9,15,x$

a
$x=17.5$

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d) $18,26,x$

a
$x=31.6$

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e) $27,51,x$

a
$x=57.7$

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f) $111,135,x$

a
$x=175$

Question ID: 30030100060

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**Question 12**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Knowledge of solving linear equations needed. *Knowledge of solving quadratic equations needed

a) $3,4,x-1$

a
$x=6$

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b) $x,12,x+8$

a
$x=5$

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c) $x+11,15,x+20$

a
$x=-3$

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d) $15,2x,2x+5$

a
$x=10$

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e) *$x+2,x+3,x+4$

a
$x=1$ or $x=-3$

(you may want to consider if $x=-3$ is a valid answer or not)

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f) *$18-x,3x,4x-6$

a
$x=8$ or $x=-6$

(you may want to consider if $x=-6$ is a valid answer or not)

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**Question 13**

Find the pronumerals

a)

a
$x=13$cm

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b)

a
$x=26$m

Question ID: 30030120020

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c)

a
$x=39$m

Question ID: 30030120030

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d)

a
$x=25$cm

$y=26$cm

Question ID: 30030120040

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e)

a
$x=61$m

$y=68$m

Question ID: 30030120050

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f)

a
$x=221$mm

or

$x=22.1$cm

Question ID: 30030120060

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**Question 14**

Find the perimeter of the following shapes

a)

a
$42$m

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b)

a
$70$cm

Question ID: 30030130020

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**Question 15**

Find the length of the diagonal in the following cuboids

a)

a
$13$m

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b)

a
$12.5$cm

Question ID: 30030140020

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**Question 16**

The dimensions for a cuboid are given (length, width and height). Find the length of the space diagonal. Calculator may be needed

a) $3,4,12$

a
$13$

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b) $8,9,12$

a
$17$

Question ID: 30030150020

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c) $12,21,28$

a
$37$

Question ID: 30030150030

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d) $9,24,32$

a
$41$

Question ID: 30030150040

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e) $5,12,84$

a
$85$

Question ID: 30030150050

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f) $28,75,180$

a
$197$

Question ID: 30030150060

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**Question 1**

__The hypotenuse is the side opposite the right angle__Which letter represents the hypotenuse in these triangles?

a)

b)

c)

d)

e)

f)

**Question 2**

__The square of the hypotenuse is equal to the sum of the squares of the other two sides__Find the area of the shaded square

a)

b)

c)

d)

e)

f)

**Question 3**

$a^2+b^2=c^2$

Find the value of $x$

a)

b)

c)

d)

e)

f)

**Question 4**

Find the value of $x$. Leave your answer as a square root

a)

b)

c)

d)

e)

f)

**Question 5**

Find the value of $x$. Calculator recommended

a)

b)

c)

d)

e)

f)

**Question 6**

Find the value of $x$. Calculator needed. Leave your answer rounded to one decimal place.

a)

b)

c)

d)

e)

f)

**Question 7**

Find the value of $x$ by finding Pythagorean Triples/Triads. No calculator

a)

b)

c)

d)

e)

f)

**Question 8**

Find the value of $x$. Calculator needed. Leave your answer rounded to two decimal places.

a)

b)

c)

d)

e)

f)

**Question 9**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. No calculator

a) $3,4,x$

b) $5,12,x$

c) $8,15,x$

d) $0.05,0.12,x$

e) $8\,000,15\,000,x$

f) $15,20,x$

g) $\frac{5}{23},\frac{12}{23},x$

h) $\frac34,1,x$

i) $9,40,x$

j) $88,165,x$

k) $\frac25,\frac34,x$

l) $\frac32,\frac{36}{7},x$

**Question 10**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Leave your answer as a square root

a) $6,11,x$

b) $9,20,x$

c) $12,13,x$

d) $1,5,x$

e) $1,1,x$

f) $13,14,x$

**Question 11**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Calculator required. Round your answer to three significant figures

a) $4,7,x$

b) $8,8,x$

c) $9,15,x$

d) $18,26,x$

e) $27,51,x$

f) $111,135,x$

**Question 12**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Knowledge of solving linear equations needed. *Knowledge of solving quadratic equations needed

a) $3,4,x-1$

b) $x,12,x+8$

c) $x+11,15,x+20$

d) $15,2x,2x+5$

e) *$x+2,x+3,x+4$

f) *$18-x,3x,4x-6$

**Question 13**

Find the pronumerals

a)

b)

c)

d)

e)

f)

**Question 14**

Find the perimeter of the following shapes

a)

b)

**Question 15**

Find the length of the diagonal in the following cuboids

a)

b)

**Question 16**

The dimensions for a cuboid are given (length, width and height). Find the length of the space diagonal. Calculator may be needed

a) $3,4,12$

b) $8,9,12$

c) $12,21,28$

d) $9,24,32$

e) $5,12,84$

f) $28,75,180$

__Answers__

**Question 1**

a) s

b) t

c) r

d) t

e) r

f) s

**Question 2**

a) $25$cm$^2$

b) $169$mm$^2$

c) $9$m$^2$

d) $36$cm$^2$

e) $16$m$^2$

f) $1$m$^2$

**Question 3**

a) $x=5$cm

b) $x=10$cm

c) $x=13$cm

d) $x=15$cm

e) $x=17$cm

f) $x=41$cm

**Question 4**

a) $x=\sqrt{13}$cm

b) $x=\sqrt{65}$mm

c) $x=\sqrt2$m

d) $x=\sqrt{97}$cm

e) $x=\sqrt{149}$m

f) $x=\sqrt{277}$mm

**Question 5**

a) $x=45$cm

b) $x=65$cm

c) $x=53$mm

d) $x=65$m

e) $x=109$cm

f) $x=145$m

**Question 6**

a) $x=5.8$cm

b) $x=8.6$inches

c) $x=12.5$m

d) $x=15.6$cm

e) $x=27.7$mm

f) $x=34.7$cm

**Question 7**

a) $x=50$cm

b) $x=0.5$cm

c) $x=0.1$m

d) $x=\frac57$cm

e) $x=1300$m or $x=1.3$km

f) $x=3.4$mm

**Question 8**

a) $x=5.02$cm

b) $x=0.44$m

c) $x=10.47$m

d) $x=14.26$mm

e) $x=2.63$km

f) $x=7.77$m

**Question 9**

a) $x=5$

b) $x=13$

c) $x=17$

d) $x=0.13$

e) $x=17\,000$

f) $x=25$

g) $x=\frac{13}{23}$

h) $x=\frac54$ or $x=1\frac14$

i) $x=41$

j) $x=187$

k) $x=\frac{17}{20}$

l) $x=\frac{75}{14}$

**Question 10**

a) $x=\sqrt{157}$

b) $x=\sqrt{481}$

c) $x=\sqrt{313}$

d) $x=\sqrt{26}$

e) $x=\sqrt2$

f) $x=\sqrt{185}$

**Question 11**

a) $x=8.06$

b) $x=11.3$

c) $x=17.5$

d) $x=31.6$

e) $x=57.7$

f) $x=175$

**Question 12**

a) $x=6$

b) $x=5$

c) $x=-3$

d) $x=10$

e) $x=1$ or $x=-3$

(you may want to consider if $x=-3$ is a valid answer or not)

f) $x=8$ or $x=-6$

(you may want to consider if $x=-6$ is a valid answer or not)

**Question 13**

a) $x=13$cm

b) $x=26$m

c) $x=39$m

d) $x=25$cm

$y=26$cm

e) $x=61$m

$y=68$m

f) $x=221$mm

or

$x=22.1$cm

**Question 14**

a) $42$m

b) $70$cm

**Question 15**

a) $13$m

b) $12.5$cm

**Question 16**

a) $13$

b) $17$

c) $37$

d) $41$

e) $85$

f) $197$

**Question 1**

__The hypotenuse is the side opposite the right angle__Which letter represents the hypotenuse in these triangles?

a)

b)

c)

d)

e)

f)

**Question 2**

__The square of the hypotenuse is equal to the sum of the squares of the other two sides__Find the area of the shaded square

a)

b)

c)

d)

e)

f)

**Question 3**

$a^2+b^2=c^2$

Find the value of $x$

a)

b)

c)

d)

e)

f)

**Question 4**

Find the value of $x$. Leave your answer as a square root

a)

b)

c)

d)

e)

f)

**Question 5**

Find the value of $x$. Calculator recommended

a)

b)

c)

d)

e)

f)

**Question 6**

Find the value of $x$. Calculator needed. Leave your answer rounded to one decimal place.

a)

b)

c)

d)

e)

f)

**Question 7**

Find the value of $x$ by finding Pythagorean Triples/Triads. No calculator

a)

b)

c)

d)

e)

f)

**Question 8**

Find the value of $x$. Calculator needed. Leave your answer rounded to two decimal places.

a)

b)

c)

d)

e)

f)

**Question 9**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. No calculator

a) $3,4,x$

b) $5,12,x$

c) $8,15,x$

d) $0.05,0.12,x$

e) $8\,000,15\,000,x$

f) $15,20,x$

g) $\frac{5}{23},\frac{12}{23},x$

h) $\frac34,1,x$

i) $9,40,x$

j) $88,165,x$

k) $\frac25,\frac34,x$

l) $\frac32,\frac{36}{7},x$

**Question 10**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Leave your answer as a square root

a) $6,11,x$

b) $9,20,x$

c) $12,13,x$

d) $1,5,x$

e) $1,1,x$

f) $13,14,x$

**Question 11**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Calculator required. Round your answer to three significant figures

a) $4,7,x$

b) $8,8,x$

c) $9,15,x$

d) $18,26,x$

e) $27,51,x$

f) $111,135,x$

**Question 12**

Find the value of $x$ so that the following three terms form a Pythagorean Triple/Triad. Knowledge of solving linear equations needed. *Knowledge of solving quadratic equations needed

a) $3,4,x-1$

b) $x,12,x+8$

c) $x+11,15,x+20$

d) $15,2x,2x+5$

e) *$x+2,x+3,x+4$

f) *$18-x,3x,4x-6$

**Question 13**

Find the pronumerals

a)

b)

c)

d)

e)

f)

**Question 14**

Find the perimeter of the following shapes

a)

b)

**Question 15**

Find the length of the diagonal in the following cuboids

a)

b)

**Question 16**

The dimensions for a cuboid are given (length, width and height). Find the length of the space diagonal. Calculator may be needed

a) $3,4,12$

b) $8,9,12$

c) $12,21,28$

d) $9,24,32$

e) $5,12,84$

f) $28,75,180$

__Answers__

**Question 1**

a) s

b) t

c) r

d) t

e) r

f) s

**Question 2**

a) $25$cm$^2$

b) $169$mm$^2$

c) $9$m$^2$

d) $36$cm$^2$

e) $16$m$^2$

f) $1$m$^2$

**Question 3**

a) $x=5$cm

b) $x=10$cm

c) $x=13$cm

d) $x=15$cm

e) $x=17$cm

f) $x=41$cm

**Question 4**

a) $x=\sqrt{13}$cm

b) $x=\sqrt{65}$mm

c) $x=\sqrt2$m

d) $x=\sqrt{97}$cm

e) $x=\sqrt{149}$m

f) $x=\sqrt{277}$mm

**Question 5**

a) $x=45$cm

b) $x=65$cm

c) $x=53$mm

d) $x=65$m

e) $x=109$cm

f) $x=145$m

**Question 6**

a) $x=5.8$cm

b) $x=8.6$inches

c) $x=12.5$m

d) $x=15.6$cm

e) $x=27.7$mm

f) $x=34.7$cm

**Question 7**

a) $x=50$cm

b) $x=0.5$cm

c) $x=0.1$m

d) $x=\frac57$cm

e) $x=1300$m or $x=1.3$km

f) $x=3.4$mm

**Question 8**

a) $x=5.02$cm

b) $x=0.44$m

c) $x=10.47$m

d) $x=14.26$mm

e) $x=2.63$km

f) $x=7.77$m

**Question 9**

a) $x=5$

b) $x=13$

c) $x=17$

d) $x=0.13$

e) $x=17\,000$

f) $x=25$

g) $x=\frac{13}{23}$

h) $x=\frac54$ or $x=1\frac14$

i) $x=41$

j) $x=187$

k) $x=\frac{17}{20}$

l) $x=\frac{75}{14}$

**Question 10**

a) $x=\sqrt{157}$

b) $x=\sqrt{481}$

c) $x=\sqrt{313}$

d) $x=\sqrt{26}$

e) $x=\sqrt2$

f) $x=\sqrt{185}$

**Question 11**

a) $x=8.06$

b) $x=11.3$

c) $x=17.5$

d) $x=31.6$

e) $x=57.7$

f) $x=175$

**Question 12**

a) $x=6$

b) $x=5$

c) $x=-3$

d) $x=10$

e) $x=1$ or $x=-3$

(you may want to consider if $x=-3$ is a valid answer or not)

f) $x=8$ or $x=-6$

(you may want to consider if $x=-6$ is a valid answer or not)

**Question 13**

a) $x=13$cm

b) $x=26$m

c) $x=39$m

d) $x=25$cm

$y=26$cm

e) $x=61$m

$y=68$m

f) $x=221$mm

or

$x=22.1$cm

**Question 14**

a) $42$m

b) $70$cm

**Question 15**

a) $13$m

b) $12.5$cm

**Question 16**

a) $13$

b) $17$

c) $37$

d) $41$

e) $85$

f) $197$

__Solutions__

**Question 1**

a)

b)

c)

d)

e)

f)

**Question 2**

a)

b)

c)

d)

e)

f)

**Question 3**

a)

b)

c)

d)

e)

f)

**Question 4**

a)

b)

c)

d)

e)

f)

**Question 5**

a)

b)

c)

d)

e)

f)

**Question 6**

a)

b)

c)

d)

e)

f)

**Question 7**

a)

b)

c)

d)

e)

f)

**Question 8**

a)

b)

c)

d)

e)

f)

**Question 9**

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k) $\frac25,\frac34,x=\frac{8}{20},\frac{15}{20},\frac{20x}{20}$

$8$ and $15$ are in a Pythagorean Triple with $17$

so $20x=17$

$x=\frac{17}{20}$

l) $\begin{align}\frac32,\frac{36}{7},x&=\frac{21}{14},\frac{72}{14},\frac{14x}{14}\\&=7\times\frac{3}{14},24\times\frac{3}{14},4\frac23x\times\frac{3}{14}\end{align}$

$7$ and $24$ are in a Pythagorean Triple with $25$

$\begin{align}4\frac23x&=25\\x&=25\div\frac{14}{3}\\&=25\times\frac{3}{14}\\x&=\frac{75}{14}\end{align}$

**Question 10**

a)

b)

c)

d)

e)

f)

**Question 11**

a)

b)

c)

d)

e)

f)

**Question 12**

a)

b)

c)

d)

e)

f)

**Question 13**

a)

b)

c)

d)

e)

f)

**Question 14**

a)

b)

**Question 15**

a)

b)

**Question 16**

a)

b)

c)

d)

e)

f)