Question 268524: A rectangular flower bed with width 12 feet and length 15 feet is going to have a walkway of uniform width on all sides. If the area of the walkway is 90 square feet, how wide is the walkway?
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! A rectangular flower bed with width 12 feet and length 15 feet is going to have a walkway of uniform width on all sides. If the area of the walkway is 90 square feet, how wide is the walkway?
Area of bed plus walkway (Abw) - Area of bed (Ab) = Area of walkway (Aw)
Abw - 15 * 12 = 90
Abw - 180 = 90
Abw = 270
(15 + 2W)(12 + 2W) = 270 (visualize or draw this, makes sense that twice the width of the walk way would be added to each of the 2 dimensions of the flower bed)
180 + 30W + 24W + 4W^2 = 270 (used foil to get this, now rearrage)
4W^2 + 54W - 90 = 0 (divide both sides by 4)
W^2 + 13.5W - 22.5 = 0
(W + 15)(W - 1.5) = 0 (15W - 1.5W = 13.5W, and 15 * -1.5 = -22.5)
since W can not be negative, W is 1.5 feet
so width of walk way is 1.5 feet
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