Geometry - Pythagoras Theorem

Answers

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 1

The hypotenuse is the side opposite the right angle
Which letter represents the hypotenuse in these triangles?

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

Question 3

$a^2+b^2=c^2$
Find the value of $x$

Question 4

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

Question 5

Find the value of $x$. Calculator recommended

Question 6

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

Question 7

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

Question 8

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

Question 9

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

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

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

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

Question 13

Find the pronumerals

Question 14

Find the perimeter of the following shapes

Question 15

Find the length of the diagonal in the following cuboids

Question 16

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

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) $197$