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MathidiaMathematics Academy
Pythagoras and right triangles
Lesson 57 of 75
Easy practice

Find the hypotenuse

Objective. Calculate a right triangle's longest side.

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  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
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Learn: the key idea

The hypotenuse is the longest side of a right-angled triangle, found opposite the right angle, and its length is calculated using a² + b² = c², where c is the hypotenuse. To find it, square both shorter sides, add the results together, then take the square root of that total. Example: for a triangle with shorter sides 6 cm and 8 cm, compute 6² + 8² = 36 + 64 = 100, then √100 = 10 cm. Always check the final answer is longer than both of the given sides, since the hypotenuse must be the largest side.

Worked example

A right-angled triangle has shorter sides of length 9 cm and 12 cm. Find the length of the hypotenuse.

Diagram of a triangle
  1. 1Square both shorter sides: 9² = 81 and 12² = 144.
  2. 2Add the squared values together: 81 + 144 = 225.
  3. 3Take the square root of the total: √225.
  4. 4The hypotenuse is 15 cm.

Answer: 15 cm

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Common mistake. Pupils often add the two shorter sides directly instead of squaring them first, giving 6 + 8 = 14 instead of the correct 10 cm; remember to square each side before adding and then take the square root.

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