the length and width of a rectangle

Question

The length of the rectangle is four times its width when the length is reduced by 2 units and the width is increased by 3 units,the area of the rectangle becomes 198 sq.units.Find the length and width of the original rectangle.

Answer 1

Let x = width, then 4x = length.  Since area is l x w we get:

 

(4x - 2)(x + 3) = 198

 

4x² + 10x - 6 = 198

4x² + 10x - 204 = 0

 

2x² + 5x - 102 = 0

 

(2x + 17)(x - 6) = 0

 

x = 6 or x = -17/2.  Since x cannot be negative, x = 6