The length of the rectangle is 3ft longer than it's width. If it's length is decreased by 3ft. and it's width increased by 2ft, it's area would be decreased by 8 square ft. What is the length of the rectangle?
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W = (L-3).
(L - 3)(W + 2) + 8 = (L)(W)
But W = (L - 3)
(L - 3)(L -1) + 8 = L(L - 3)
L^2 - 4L +11 = L^2 -3L
L = 11
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The length is 3ft longer than width. So width is (L - 3) and length is just (L).
If the length is decreased by 3 (which will now make L - 3) and width is increased by 2 (so (L - 3) + 2), the area of the altered rectangle is now (L - 3) * (L - 3 + 2), which is just (L - 3)(L -1). This rectangle is 8 square feet short of the area of the first rectangle, which is just (L)(L - 3)
Equating them gives the equation (L)(L - 3) = (L -3)(L -1) + 8. Now just solve for L.