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13.02 Finding the hypotenuse

Worksheet
Hypotenuse
1

Find the length of the hypotenuse in each of the following right-angled triangles:

a
b
c
d
2

Find the exact value of c for the following right-angled triangles:

a
b
c
d
3

Find the value of c for the following triangles, correct to two decimal places:

a
b
4

For each of the following right-angled triangles, find the length of the hypotenuse, c, given the other two sides. Round your answers to two decimal places.

a

4 and 7

b

15 and 16

c

7 and 10

d

15 and 22

Perimeter
5

Consider the following triangle:

a

Find the length of the hypotenuse.

b

Find the perimeter of the triangle.

6

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.

b

Find the perimeter of the triangle.

7

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

a

Find the length of its hypotenuse.

b

Find the perimeter of the triangle.

Applications
8

Find the number that completes the following Pythagorean triads given its two smallest numbers:

a

5 and 12

b

9 and 40

9

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

a

A rectangle has side lengths 5 and 12.

b

A rectangle has side lengths 9 and 14.

10

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

a

A square has a side length of 7.

b

A square has a side length of 11.

11

Complete the following table, rounding the values to one decimal place:

Side length of squareExact length of diagonal
1
3
7
11
249
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Outcomes

MA4-16MG

applies Pythagoras' theorem to calculate side lengths in right-angled triangles, and solves related problems

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