A rectangle is twice as long as it is wide. If its length is increased by 4 inches and its width is increased by 2 inches, its area is increased by 64 in^2. Find its original dimensions.

Original rectangle is 4w by w

Changed rectangle is 4w+4 by w-1

This rectangle area is 60= (4w+4)(w-1)

60 = 4w^2 + 4w -4w - 4

60 = 4 w^2 - 4 divide all by 4

15 = w^2 -1

0= w^2 - 16

0 = (w+4)(w-4)

w = 4 or -4 in this case w can’t be a negative

So, original dimensions are 16 long by 4 wide

Step-by-step explanation:

I hope this makes sense