High School

The dimensions of a rectangle are such that its length is 3 inches more than its width. If the length were doubled and the width were decreased by 1 inch, the area would be increased by 176 square inches. What are the length and width of the rectangle?

Answer :

Length (L): w + 3 ⇒2(w + 3)

width (w): w ⇒ w - 1

Area (A) = L x w

A = (w + 3)(w)

A = w² + 3w

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A + 176 = 2(w + 3)(w - 1)

(w² + 3w) + 176 = 2(w + 3)(w - 1)

w² + 3w + 176 = 2w² + 4w - 6

3w + 176 = w² + 4w - 6

176 = w² + w - 6

0 = w² + w - 182

0 = (w - 13) (w + 14)

0 = w - 13 0 = w + 14

w = 13 w = -14

Since width cannot be negative, disregard -14

w = 13

Length (L): w + 3 = (13) + 3 = 16

Answer: width = 13 in, length = 16 in

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