Maths Library

Pythagorean Theorem: Grade 8 math

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

Pythagorean Theorem is taught in Grade 8 (age 13 to 14) 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 Common Core State Standards. Check wording and codes against the official document.

  • 8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems.

Sample sheet and answers

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

Pythagorean Theorem

Grade 8 math

Qs
6
Marks
12
NameDateScore / 12
1.
A right-angled triangle has shorter sides 9 cm and 12 cm. Find the hypotenuse.
[2]
2.
A right-angled triangle has shorter sides 5 cm and 12 cm. Find the hypotenuse.
[2]
3.
A right-angled triangle has shorter sides 8 cm and 15 cm. Find the hypotenuse.
[2]
4.
A right-angled triangle has shorter sides 8 cm and 15 cm. Find the hypotenuse.
[2]
5.
A right-angled triangle has shorter sides 8 cm and 15 cm. Find the hypotenuse.
[2]
6.
A right-angled triangle has shorter sides 3 cm and 4 cm. Find the hypotenuse.
[2]

Answer key

  1. 15 cmc2 = 92 + 122 = 81 + 144 = 225; c = 15 cm
  2. 13 cmc2 = 52 + 122 = 25 + 144 = 169; c = 13 cm
  3. 17 cmc2 = 82 + 152 = 64 + 225 = 289; c = 17 cm
  4. 17 cmc2 = 82 + 152 = 64 + 225 = 289; c = 17 cm
  5. 17 cmc2 = 82 + 152 = 64 + 225 = 289; c = 17 cm
  6. 5 cmc2 = 32 + 42 = 9 + 16 = 25; c = 5 cm