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3.02 Finding the hypotenuse

Worksheet
Hypotenuse
1

For each of the following, find the number that completes a Pythagorean triple given the two smallest numbers:

a

3 and 4

b

8 and 6

c

9 and 12

d

8 and 15

2

For each diagram, identify which side of the triangle is the hypotenuse.

a
b
3

For the following right-angled triangles:

i

Write the equation that the sides of the triangle satisfy.

ii

Solve the equation to find the length of the hypotenuse.

a
b
c
4

Find the length of the unknown side of the following triangles:

a
b
c
d
e
f
5

Find the length of the unknown side of the following triangles as a surd:

a
b
6

Find the length of the unknown side of the following triangles, correct to two decimal places:

a
b
c
d
e
f
g
h
Perimeter
7

Consider the following triangle:

a

Find the length of the hypotenuse.

b

Find the perimeter of the triangle.

8

A right-angled triangle has two shorter sides measuring 15.4 \,\text{mm} and 17.7 \,\text{mm}.

a

Find the length of the hypotenuse, correct to two decimal places.

b

Find the perimeter of the triangle, correct to two decimal places.

9

A right isosceles triangle has two sides measuring 17 \,\text{cm}.

a

Find the length of its hypotenuse, correct to two decimal places.

b

Find the perimeter of the triangle, correct to two decimal places.

Diagonals of rectangles
10

Find the exact length of the diagonals of the following rectangles:

a

A rectangle whose side lengths are 9 and 12.

b

A rectangle whose side lengths are 9 and 14.

11

Find the length of the diagonals of the following squares, correct to two decimal places:

a

A square with side length of 9.

b

A square with side length of 12.

12

Complete the following table:

Side length of squareExact length of diagonal
1
3
6
11
249
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VCMMG318

Investigate Pythagoras’ Theorem and its application to solving simple problems involving right-angled triangles.

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