The length of a rectangle is 4 inches more than twice the width. If the area of the rectangle is 48 square inches, what is the length of the rectangle?

Question

Story problem involving area.

Answer 1

L = 2W + 4

Area = 48 = LW

 

Using substitution

48 = (2W+4)(W) 

48 = 2W²+4W

 

and 0 = 2W²+4w-48

 

Dividing by 2

0 = W²+2W-24

 

This factors into

0 = (W+6)(W-4)

Setting each factor equal to 0

W+6 = 0  and W-4=0

W = -6, 4

 

But -6 is not a possible solution since a measurement of length or width cannot be negative.

 

So W = 4

L = 2W+4 = 2(4)+4 = 12

 

and 12(4) = 48, the area.