The length of the smaller rectangle at the right is 1 inch less than twice its width. 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 larger rectangle?
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The length of the smaller rectangle at the right is 1 inch less than twice its width. 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 are the dimensions of the smaller rectangle?
What shaded region?
I will assume that the smaller rectangle is inside the larger, and the "shaded" region is the difference in their areas, so ...
(2x+1)(x+2) - (2x-1)(x) = 86
2x^2 + 5x + 2 - 2x^2 + x - 86 = 0
6x = 84
x = 14
the smaller is 14 by 27
(2x+1)(x+2) - (2x-1)(x) = 86
2x^2 + 5x + 2 - 2x^2 + x - 86 = 0
6x = 84
x = 14
the smaller is 14 by 27
14 by 27
2+2=4
1 answer