The length of a rectangle is 3 m more than double the width, and the area of the rectangle is 54 m^2. Find the dimensions of the rectangle.

Answer 1

L = 2 W + 3

A = L * W = ( 2 W + 3 ) * W = 2 W ^ 2 + 3 W

A = 2 W ^ 2 + 3 W

54 = 2 W ^ 2 + 3 W Subtract 54 to both sides

54 - 54 = 2 W ^ 2 + 3 W - 54

0 = 2 W ^ 2 + 3 W - 54

2 W ^ 2 + 3 W - 54 = 0

The solutions are :

W = - 6

and

W = 9 / 2

Width can't be negative so :

W = 9 / 2 = 4.5 m

L = 2 W + 3 = 2 * ( 9 / 2 ) + 3 = 9 + 3 = 12 m

A = L * W = 12 * 9 / 2 = 108 / 2 = 54 m ^ 2