# The perimeter of a rectangle is 54 inches and its area is 182 square inches. How do you find the length and width of the rectangle?

The sides of the rectangle are 13 and 14 inches.

#### Explanation:

$2 a + 2 b = 54$
$a \times b = 182$

$a = \frac{182}{b}$

$2 \times \left(\frac{182}{b}\right) + 2 b = 54$

$\frac{364}{b} + 2 b = 54$

Multiplying by "b":

$364 + 2 {b}^{2} = 54 b$

$2 {b}^{2} - 54 b + 364 = 0$

Solving the quadratic equation:

${b}_{1} = 14$
${a}_{1} = \frac{182}{14} = 13$

${b}_{2} = 13$
${a}_{2} = \frac{182}{13} = 14$

The sides of the rectangle are 13 and 14 inches.