Question 300606
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