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Question

A homeowner has poured a rectangular concrete slab in her backyard to use for a barbecue area. The length is 3 feet more than its width. There is a 2ft wide flower bed around the barbecue area. If the area covered by the barbecue area and the flower bed is 270 square feet, find the dimensions of the barbecue area.

Answer 1

Let w be the width.
Then the length = w + 3
Total area:
(w + 4)((w + 3) + 4) = 270
(w + 4)(w + 7) = 270
w^2 + 11w + 28 = 270
w^2 + 11w -242 = 0
Use the quadratic formula:
w = [-11 +/- √(121 + 4(242))]/2
w = (-11 +/- √1089)/2
w = 11, -22 [extraneous]
length = 11 + 3 = 14