Length of a rectangular garden is 8ft longer than the width. The garden is surrounded by a sidewalk it is 4ft wide area of 320 square ft. Find the dimersions

Let the garden dimensions be x (the length) and w (the width). Then w = x - 8 and together with the sidewalk it forms a larger rectangle whose length is x + 8 (add twice the width of the sidewalk) and the width is x (add twice the width of the sidewalk to the original width, w + 2*4 = x - 8 + 8). The area of the sidewalk is the difference of the areas of the larger rectangle, (x + 8)x, and the smaller rectangle, x(x - 8). Thus,

(x + 8)x - x(x - 8) = 320; open the parentheses

x^2 + 8x - x^2 + 8x = 320; simplify

16x = 320; x = 20

Answer: the length of the garden is 20 ft and the width is 12 ft.

May 12th, 2015

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