# Using the Pythagorean Theorem, how do you find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long?

Mar 7, 2016

The other leg is $6$ feet long.

#### Explanation:

Pythagorean Theorem tells that in a right angled triangle, sum of the squares of two perpendicular lines is equal to the square of hypotenuse.

In the given problem, one leg of a right triangle is $8$ feet long and the hypotenuse is $10$ feet long,. Let the other leg be $x$, then under the theorem

${x}^{2} + {8}^{2} = {10}^{2}$ or ${x}^{2} + 64 = 100$ or ${x}^{2} = 100 - 64 = 36$ i.e.

$x = \pm 6$, but as $- 6$ is not permissible, $x = 6$ i.e.

The other leg is $6$ feet long.