Maths Library

Pythagoras' Theorem: Year 9 maths

This topic covers applying Pythagoras' theorem to find unknown side lengths in right-angled triangles. The worksheet practises calculating the hypotenuse, finding a shorter leg, and solving simple applied context problems.

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What this covers

Pythagoras' Theorem is taught in Year 9 (age 14 to 15) as a topic to introduce. It sits in the Geometry strand.

Worked example

A right-angled triangle has shorter sides of length 6 cm and 8 cm. Calculate the length of the hypotenuse c.

  1. State Pythagoras' theorem: a^2 + b^2 = c^2
  2. Substitute side lengths: 6^2 + 8^2 = 36 + 64 = 100
  3. Take the square root: c = sqrt(100) = 10

Answer: 10

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Calculating hypotenuse using Pythagorean triples with whole number answers
  2. Calculating a shorter leg with whole number answers
  3. Finding hypotenuse requiring square root rounding to 1 decimal place
  4. Finding shorter leg requiring rounding to 1 decimal place
  5. Multi-step word problems or finding distance between coordinate points

Common mistakes

  • Adding side lengths before squaring instead of squaring first
  • Adding squares when calculating a shorter side instead of subtracting

Curriculum links

Indicative matches to Australian Curriculum v9. Check wording and codes against the official document.

  • AC9M9SP01 Apply Pythagoras' theorem to find unknown side lengths in right-angled triangles in practical situations.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Pythagoras' Theorem

Year 9 maths

Qs
6
Marks
18
NameDateScore / 18
1.
A right-angled triangle has hypotenuse 15 cm and one side 9 cm. Find the other side.
[3]
2.
A right-angled triangle has hypotenuse 13 cm and one side 5 cm. Find the other side.
[3]
3.
A right-angled triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.
[3]
4.
A right-angled triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.
[3]
5.
A right-angled triangle has hypotenuse 17 cm and one side 8 cm. Find the other side.
[3]
6.
A right-angled triangle has shorter sides 3 cm and 4 cm. Find the hypotenuse.
[3]

Answer key

  1. 12 cmb2 = 152 − 92 = 225 − 81 = 144; b = 12 cm
  2. 12 cmb2 = 132 − 52 = 169 − 25 = 144; b = 12 cm
  3. 15 cmb2 = 172 − 82 = 289 − 64 = 225; b = 15 cm
  4. 15 cmb2 = 172 − 82 = 289 − 64 = 225; b = 15 cm
  5. 15 cmb2 = 172 − 82 = 289 − 64 = 225; b = 15 cm
  6. 5 cmc2 = 32 + 42 = 9 + 16 = 25; c = 5 cm