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Pythagorean theorem: find the hypotenuse, step by step

The hypotenuse is the longest side of a right triangle: square the two legs, add them, then take the square root.

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The question
3016? cm

Right triangle, 16 and 30

1630?
  1. The hypotenuse is the side OPPOSITE the right angle — never one of the two that make the corner. It is also always the longest, so you can check yourself twice.
  2. Here the hypotenuse is the missing one, so the two given sides are both legs: 16 and 30.
  3. Square the two you have: 16² = 256 and 30² = 900.
  4. The two squares ADD to the square on the hypotenuse: 256 + 900 = 1156.
  5. That is the square, not the side. Take the square root: √1156 = 34 cm.

How it works.

  1. 01

    The hypotenuse is the side OPPOSITE the right angle — never one of the two that make the corner. It is also always the longest, so you can check yourself twice.

  2. 02

    Here the hypotenuse is the missing one, so the two given sides are both legs: 16 and 30.

  3. 03

    Square the two you have: 16² = 256 and 30² = 900.

  4. 04

    The two squares ADD to the square on the hypotenuse: 256 + 900 = 1156.

  5. 05

    That is the square, not the side. Take the square root: √1156 = 34 cm.

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