Finding the hypotenuse | Year 8

01 / LEARN

The idea, step by step

Use addition for the longest side

When both legs are known, square each and add. This finds the square of the hypotenuse. Take the positive square root because an ordinary side length is positive.

Use consistent units before squaring. A calculation combining 3 metres and 400 centimetres without conversion compares unlike quantities.

Check size and units

The answer must exceed either leg but be less than their sum. A result of 25 cm for legs 3 cm and 4 cm is the squared number mistaken for a length.

Squared lengths carry square units during the calculation; after taking the square root, give ordinary length units.

c = \sqrt{a^{2} + b^{2}}

A common trap

Stopping at $c^{2} = 225$ and calling the length 225 cm.

Instead: The squared equation requires a square root: c = 15 cm.

02 / WORKED EXAMPLES

See the thinking

Example 1

A familiar triple

Find the hypotenuse for legs 9 cm and 12 cm.

Square and add: $c^{2} = 81 + 144 = 225$ .
Take the positive root: c = 15.
Fifteen is larger than 12 and smaller than 21.

15 cm.

Example 2

Convert first

A right triangle has legs 3 m and 400 cm. Find its hypotenuse.

Convert 400 cm to 4 m.
Calculate $c^{2} = 3^{2} + 4^{2} = 25$ .
Take the square root and retain metres.

5 m, or 500 cm.

Check your understanding

Find c for legs 5 cm and 12 cm.

Show answer

13 cm.

The squared sum is $25 + 144 = 169$ .

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Find the hypotenuse for legs 6 cm and 8 cm.
2 marks
Find the hypotenuse for legs 8 m and 15 m.
2 marks
Find the hypotenuse for legs 7 cm and 24 cm.
2 marks
Find the hypotenuse for legs 1.5 m and 2 m.
2 marks
Find the hypotenuse for legs 60 cm and 0.8 m.
3 marks
A student finds c = 7 cm for legs 8 cm and 15 cm. Explain the size check and correct the answer.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find the hypotenuse for legs 6 cm and 8 cm.
2 marks
$c^{2} = 36 + 64 = 100$ .
Take the positive square root.
10 cm.
Find the hypotenuse for legs 8 m and 15 m.
2 marks
$c^{2} = 64 + 225 = 289$ .
The positive root is 17.
17 m.
Find the hypotenuse for legs 7 cm and 24 cm.
2 marks
$c^{2} = 49 + 576 = 625$ .
The positive root is 25.
25 cm.
Find the hypotenuse for legs 1.5 m and 2 m.
2 marks
$c^{2} = 2.25 + 4 = 6.25$ .
The positive root is 2.5.
2.5 m.
Find the hypotenuse for legs 60 cm and 0.8 m.
3 marks
Convert 60 cm to 0.6 m.
$c^{2} = 0.36 + 0.64 = 1$ .
1 m, or 100 cm.
A student finds c = 7 cm for legs 8 cm and 15 cm. Explain the size check and correct the answer.
3 marks
The size check already rejects 7.
Compute $64 + 225 = 289$ and take the root.
The hypotenuse cannot be shorter than either leg; c = 17 cm.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics (2026)

Hypotenuse and right-angled triangles; why the theorem works; finding the hypotenuse; finding a shorter side; exact roots versus rounded answers; checking whether a triangle is right-angled; practical length problems.

Official curriculum source ↗

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