A rectangle is twice as long as it is wide. If the length and width are both increased by 3 cm, the area is increased by 72cm^2.

Question

How do I find the original dimensions?

Answer 1

Hi, Anita

 

Okay, so the area of a rectangle A = l x w

 

IF length and width are both increased by 3 cm, the area is increased by 72 cm²

 

A = (l + 3 ) x (w + 3) = l x w + 72

lw + 3 l + 3w + 9 = lw + 72

3l + 3w = 63

3(l + w) = 63

l + w = 21

 

Since l = 2w  (the rectangle is twice as long as it is wide)

 

then 2w + w = 21

3w = 21

w = 7

 

width is 7 cm

length is 14 cm