# One leg is 12 inches and the hypotenuse is 13 inches. How do you find the missing leg?

Mar 8, 2018

Recall that the sum of the squares of the legs is equal to the square of the hypotenuse in a right triangle

#### Explanation:

Thus, the square of 13 is equal to the square of 12 plus the square of the missing leg.

We can set up an equation with x as the unknown length.

${x}^{2} + {12}^{2} = {13}^{2}$

${x}^{2} + 144 = 169$

${x}^{2} = 25$

$x = \pm 5$ Disregard the $- 5$ because a side cannot have a negative length

Thus, the missing side is 5 inches.