# How do you find the hypotenuse if the length of the legs of a right triangle are 30 ft and 40 ft?

Dec 31, 2015

Use the Pythagorean Theorem, which relates the lengths of the sides in a right triangle.

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

Where $a , b$ are legs and $c$ is the hypotenuse.

$a = 30$
$b = 40$
c=?

Plug these values into the equation.

${30}^{2} + {40}^{2} = {c}^{2}$

$900 + 1600 = {c}^{2}$

$2500 = {c}^{2}$

$\sqrt{2500} = c$

color(red)(c=50

Note that this is a common right triangle pattern, where the side lengths are $3 , 4 , 5$. This time, all the sides are just $10$ times larger.