# The hypotenuse of an isosceles right triangle is 12 inches. What is the length of each leg?

Jan 8, 2017

Length of each leg is $8.4852$ inches.

#### Explanation:

In a right triangle, square on the hypotenuse is equal to sum of the squares on the other two sides.

Here, other two sides as it is an isosceles right triangle. Let these sides be each $x$ inches.

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

or $2 {x}^{2} = 144$

or ${x}^{2} = 72$

i.e. $x = \sqrt{72} = 6 \sqrt{2} = 6 \times 1.4142 = 8.4852$

Hence, length of each leg is $8.4852$ inches.