The area of a rectangle is 28 square inches. The length is 8 more than thrice the width. How do you find the length and the width?

May 21, 2018

Width = $2$
Length = $14$

Explanation:

Length: $L = 3 x + 8$
Width: $W = x$

Area of Rectangle = $L W$
$28 = \left(3 x + 8\right) x$
$28 = 3 {x}^{2} + 8 x$
$0 = 3 {x}^{2} + 8 x - 28$
$0 = \left(3 x + 14\right) \left(x - 2\right)$

$3 x + 14 = 0 \to x = - \frac{14}{3}$
But Width can't be negative.

$x - 2 = 0 \to x = 2$
So Width is $2$ and Length is $3 \left(2\right) + 8 = 14$