SOLUTION: A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path? Taken from B

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Question 89359: A garden area is 30 ft long and 20 ft wide. A path of uniform width
is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path?
Taken from Beginning Algebra 6th Edition Ch. 10 Pg.835
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
let w equal the width of the path ... the dimensions of the remaining garden area are 30-2w long and 20-2w wide

(30-2w)(20-2w)=400 ... FOILing gives 600-100w+4w^2=400 ... dividing by 4 gives 150-25w+w^2=100 ... w^2-25w+50=0

quadratic formula gives w=%2825+%2B-+sqrt%2825%5E2-4%2A1%2A50%29%29%2F%282%2A1%29=%2825+%2B-+5sqrt%2817%29%29%2F2, so w=2.19 (approximately)