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Let the length be l, the width be w, and the area be A. The equation for the area of a rectangle is A = l*w; we know A = 77, so we need to get l in terms of w so we only have one variable to solve for. We're given l = 2w-3, so we can substitute back in:

A=77=(2w-3)*w

77=2w^2-3w

0=2w^2-3w-77

0=(2w+11)*(w-7)

so w=-5.5 or w=7. Since we can't have a negative width, w=7 inches. Plugging back in to our equation for l and w: l=2w-3=2(7)-3=14-3=11, so the length is 11 inches.

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