Geometry - Pythagoras Theorem
Question 1
The hypotenuse is the side opposite the right angleWhich 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 sidesFind 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)
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$9$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)
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$1$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)
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$x=10$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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$x=17$cm
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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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$x=\sqrt{149}$m
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f)
a
$x=\sqrt{277}$mm
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Question 5
Find the value of $x$. Calculator recommended
a)
a
$x=45$cm
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b)
a
$x=65$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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$x=109$cm
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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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$x=\frac57$cm
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$x=1300$m or $x=1.3$km
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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)
a
$x=0.44$m
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c)
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$x=10.47$m
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d)
a
$x=14.26$mm
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$x=2.63$km
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a
$x=7.77$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
$x=\frac{17}{20}$
Question ID: 30030080110
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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
$x=\sqrt2$
Question ID: 30030090050
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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
$x=8.06$
Question ID: 30030100010
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b) $8,8,x$
a
$x=11.3$
Question ID: 30030100020
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c) $9,15,x$
a
$x=17.5$
Question ID: 30030100030
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d) $18,26,x$
a
$x=31.6$
Question ID: 30030100040
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e) $27,51,x$
a
$x=57.7$
Question ID: 30030100050
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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
$x=6$
Question ID: 30030110010
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b) $x,12,x+8$
a
$x=5$
Question ID: 30030110020
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c) $x+11,15,x+20$
a
$x=-3$
Question ID: 30030110030
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d) $15,2x,2x+5$
a
$x=10$
Question ID: 30030110040
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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)
Question ID: 30030110050
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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)
Question ID: 30030110060
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Question 13
Find the pronumerals
a)
a
$x=13$cm
Question ID: 30030120010
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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
Question ID: 30030130010
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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
Question ID: 30030140010
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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
$13$
Question ID: 30030150010
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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
$85$
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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 angleWhich 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 sidesFind 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 angleWhich 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 sidesFind 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
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b)
c)
d)
e)
f)
Question 3
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b)
c)
d)
e)
f)
Question 4
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b)
c)
d)
e)
f)
Question 5
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b)
c)
d)
e)
f)
Question 6
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b)
c)
d)
e)
f)
Question 7
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b)
c)
d)
e)
f)
Question 8
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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)