# If one leg of a triangle is 4 feet and the other leg is 12 feet, what is the hypotenuse?

Jan 2, 2016

$4 \sqrt{10} \approx 12.6491$

#### Explanation:

The Pythagorean Theorem states that

${a}^{2} + {b}^{2} = {c}^{2}$

where $a , b$ are legs in a right triangle and $c$ is the hypotenuse (the longest side).

So, we know that $a = 4$ and $b = 12$ and we want to find $c$.

${4}^{2} + {12}^{2} = {c}^{2}$

$16 + 144 = {c}^{2}$

${c}^{2} = 160$

$c = \sqrt{160}$

$c = \sqrt{16 \times 10}$

$c = \sqrt{16} \times \sqrt{10}$

$c = 4 \sqrt{10} \approx 12.6491$