# A right triangle has a hypotenuse of 25 feet and a leg of 7 feet. What is the length of the other leg?

Mar 21, 2018

24 ft

#### Explanation:

The Pythagorean theorem states that the sum of the squares of the two legs is equal to the hypotenuse squared.

${7}^{2} + {x}^{2} = {25}^{2} \rightarrow$ I'll use x to represent the unknown leg.

$49 + {x}^{2} = 625$

${x}^{2} = 576$

$x = \pm 24 \rightarrow$ Eliminate the -24 answer choice; a side length cannot be negative

The other leg is 24 ft.

Mar 21, 2018

$24 \text{ feet}$

#### Explanation:

$\text{Apply "color(blue)"Pythagoras' theorem ""to the triangle}$

$\text{let the length of unknown leg be x}$

$\Rightarrow {25}^{2} = {7}^{2} + {x}^{2}$

$\Rightarrow {x}^{2} = {25}^{2} - {7}^{2}$

$\Rightarrow x = \sqrt{625 - 49} = \sqrt{576} = 24 \text{ feet}$