Finding the Dimension of the Rectangle

Question

The length of a rectangle is 4 times greater than its width. if the length is increased by 2 and the width is increased by 3, the area is increased by 58 square units. What is the original dimension of the rectangle?

Answer 1

L=4w

A= l*w= 4w^2

(L+2)*(w+3)=4w^2

(4w+2)*(w+3)=4w^2+58

4w^2+14w+6=4w^2+58

14w=52

W=52/14=26/7 <-- original width

L= 104/7 <-- original length

Area= 2704/49 <-- original area

L+2= 118/7

W+3= 47/7

New area= 5546/49

The difference of these areas is 2842/49=58