# The length of Dana's rectangular living room is 12 feet and the distance between opposite corners is 20 feet. What is the width of Dana's living room?

Dec 1, 2016

The width of Dana's living room is 16 feet.

#### Explanation:

Because Dana's living room is rectangular and we are given the length of one side and the length of the diagonal we can use the Pythagorean Theorem to solve this problem.

For a right triangle which the length, width and diagonal make up the Pythagorean Theorem states:
${a}^{2} + {b}^{2} = {c}^{2}$

Let the length of 12 be $a$ and because the diagonal is the hypotenuse of the triangle (the side opposite the right angle) we let $c$ be 20. Substituting and solving gives:

${12}^{2} + {b}^{2} = {20}^{2}$

$144 + {b}^{2} = 400$

$144 - 144 + {b}^{2} = 400 - 144$

$0 + {b}^{2} = 256$

${b}^{2} = 256$

$\sqrt{{b}^{2}} = \sqrt{256}$

$b = 16$