# The length of a rectangle is 3 inches more than twice the width. The area is 27 square inches. What is the length?

Jun 4, 2016

Length $= 6 \in c h e s$

#### Explanation:

Area
$l \times b = 27$ ---------(1)

Length

$l = 2 b + 3$
Substituting $l = 2 b + 3$ in equation (1)

$\left(2 b + 3\right) \times b = 27$
$2 {b}^{2} + 3 b = 27$
$2 {b}^{2} + 3 b - 27 = 0$
$2 {b}^{2} + 9 b - 6 b - 27 = 0$
$2 b \left(b + 9\right) - 3 \left(2 b + 9\right) = 0$
$\left(2 b - 3\right) \left(b + 9\right) = 0$
$.2 b - 3 = 0$
$2 b = 3$
$b = \frac{3}{2}$
$b + 9 = 0$
$b = - 9$

width cannot be negative. Hence
Width $= \frac{3}{2}$

Then Lenth

$l = 2 b + 3$
$l = \left(2 \times \frac{3}{2}\right) + 3$
$l = \frac{6}{2} + 3 = 3 + 3 = 6$