SOLUTION: A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30 ft by 40 ft. The total area, garden plus walkway, is to be 1800 ft2. What

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Question 48477: A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30 ft by 40 ft. The total area, garden plus walkway, is to be 1800 ft2. What must be the width of the walkway to the nearest thousandth?

Thanks
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The walk is of width x on all sides, so the new width and length are
30 + 2x and 40 + 2x
+%2830+%2B+2x%29%2A%2840+%2B+2x%29+=+1800
1200+%2B+80x+%2B+60x+%2B+4x%5E2+=+1800
4x%5E2+%2B+140x+-+600+=+0
x%5E2+%2B+35x+-+150+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a = 1
b = 35
c = -150
x+=+%28-35+%2B-+sqrt%28+35%5E2-4%2A1%2A%28-150%29+%29%29%2F%282%2A1%29+
%28-35+%2B-+sqrt%281225+%2B+600%29%29+%2F+2
%28-35+%2B-+42.72%29+%2F+2
7.72%2F2
3.860 the width of the walk
check
(30 + 7.72)*(40 + 7.72) = 1800
1800 = 1800
OK