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

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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.

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