Question

The leng of the smaller rectangle is 1 inch less than twice its wide. both the dimensions of the larger rectangle are 2 inches longer than the smaller rectangle. the area of the shaded region is 86 square inches. what is the area of the smaller rectangle?

Answer 1

assuming the smaller rectangle is enclosed by the larger, we have

small rectangle: w(2w-1)
large rectangle: (w+2)(2w-1+2)

Assuming the shaded region is the difference between the two rectangles, we have

(w+2)(2w+1)-w(2w-1) = 86
w = 14

So, the smaller is 14x27, with area=378