SOLUTION: A landscaper designed a garden such that a grass path of uniform width surrounds a rectangular fountain. The fountain is 60m long & 40m wide, & the area of the graa path is 616m^2.

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Question 300606: A landscaper designed a garden such that a grass path of uniform width surrounds a rectangular fountain. The fountain is 60m long & 40m wide, & the area of the graa path is 616m^2. Determine the width of the grass path
Answer by alanc(27) About Me  (Show Source):
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Miscellaneous_Word_Problems/300606 (2010-05-04 19:55:27): A landscaper designed a garden such that a grass path of uniform width surrounds a rectangular fountain. The fountain is 60m long & 40m wide, & the area of the graa path is 616m^2. Determine the width of the grass path


60 by 40
616 square meters
x * y = A; A - 60*40 = 616
x = 60 + 2l
y = 40 + 2l
Since the width of the grass path is constant, I'll name it l and it augments the original fountain length and width by 2l.
(60 + 2l)*(40 + 2l) = 60*40 + 616
(fountain area plus grass path area should equal the new length * new width).
60*40 + 616 = 2400 + 616 = 3016.
2400 + 4*l*l + 120*l + 80*l = 2400 + 4*l*l + 200*l = 3016
we have 4*l*l + 200*l -616 = 0
l = -200/(2*4) + [sqrt(200*200 - 4*4*(-616))] /(2*4)
l = -25 + sqrt(49856) / 8
l = -25 + 223.28457179124580079903972119481 / 8
l = 27.910571473905725099879965149351 - 25
l = 2.9105 m