Problema Solution
the length of the smaller rectangle at the right is 1 in leass that twice its width. Bothe 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 are the dimensions of the smaller rectangle?
Answer provided by our tutors
For the smaller inside rectangle
Width is x
Length is 2x-1
Therefore its area is (2x-1)(x), = 2x^2-x
For the larger outside rectangle
Width is x+2
Length is 2x-1+2, or 2x+1
Therefore area is (x+2)(2x+1)' = 2x^2+5x+2
The difference in their areas is 86
Therefore (2x^2+5x+2) -(2x^2-x) = 86
2x^2+5x+2-2x^2+x = 86
6x=84
x=14
The area of the smaller rectangke is (2x-1)(x)
=2(14)^2-14
=378 in^2,