# What is the width of a rectangle if the diagonal is 28 and the length is 19?

Jun 29, 2016

$w = 3 \sqrt{47}$

width $= 20.57$

#### Explanation:

The diagonal of a rectangle creates a right triangle, allowing us to use the Pythagorean Theorem to solve for the missing side.

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

${w}^{2} + {l}^{2} = {d}^{2}$

$d = 28$
$l = 19$
w=?

${w}^{2} + {19}^{2} = {28}^{2}$

${w}^{2} + 361 = 784$

${w}^{2} \cancel{+ 361} \cancel{- 361} = 784 - 361$

${w}^{2} = 423$

$w = \sqrt{423}$

$w = \sqrt{3 \cdot 3 \cdot 47}$

$w = 3 \sqrt{47}$

width $= 20.57$