Question

The dimensions of a rectangle are such that its length is 3 in more than its width if the length were doubled and if the width were decreased by 1 in the area would be increased by 176in what are the length and width of the rectangle

Answer 1

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