Pythagoras’ theorem

In a right-angled triangle, the square on the longest side (the hypotenuse) equals the squares on the other two sides added together.

Key facts

  • a^2 + b^2 = c^2, where c is the hypotenuse.
  • The hypotenuse is opposite the right angle and always the longest side.
  • Finding a shorter side? Subtract instead: a^2 = c^2 − b^2.

Worked examples

Example 1

Find the hypotenuse c when the other sides are 6 cm and 8 cm.

  1. Square the two shorter sides. 6^2 = 36, 8^2 = 64
  2. Add them. 36 + 64 = 100
  3. Square root. c = √100 = 10 cm

Answer: c = 10 cm

Questions about pythagoras’ theorem