The area of a rectangle is 14 m2 , and the length of the rectangle is 3 m less than twice the width. Find the dimensions of the rectangle.

Question

The area of a rectangle is
14 m2
, and the length of the rectangle is
3 m
less than twice the width. Find the dimensions of the rectangle.

Answer 1

Let W = width and L = length 

 

length is 3 less than twice width  ==>  L = 2*W - 3

 

Area = L*W = (2*W-3)*W = 14 

2*W^2 -3*W - 14 = 0

(2W - 7)*(W + 2) = 0 

2W - 7 = 0  or  W + 2 = 0

W = 7/2  or  W = -2

Width cannot be negative so W = 7/2 = 3.5

So L = 2*(7/2) - 3 = 7 - 3 = 4

 

The length is 4 m and the width is 3.5 m  

 

Check:  2*(3.5) - 3 = 4, length is 3 less than twice width

            Area = L*W = 4*3.5 = 14 m^2