Question

A rectangle has a length 5 feet greater than its width. If both dimensions are increased by 2 feet, write an expression for the difference in the areas of the rectangle

Answer 1

W
L = W +5 
New dimensions:
L' = L+2 = W+5+2 = W +7
W' = W+ 2 

A = W(W+5)
A' = (W+2)(W+7)
A' - A = (W+2)(W+7) - W(W+5) 
         = W^2 + 9W +14 - W^2 - 5W
         = 4W + 14