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 mu

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Question 683894: 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?
a. 7.720 ft
b. 5.430 ft
c. 3.860 ft
d. 2.610 ft
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Let the width of the walkway be xft
Then, %2830+%2B+2x%29%2840+%2B+2x%29+=+1800
Or 2%2815+%2B+x%29%2A2%2820+%2B+x%29+=+1800
4%2815+%2B+x%29%2820+%2B+x%29+=+1800
cross%284%29%2815+%2B+x%29%2820+%2B+x%29+=+cross%281800%29450
%2815+%2B+x%29%2820+%2B+x%29+=+450
x%5E2+%2B+35x+%2B+300+=+450
x%5E2+%2B+35x+%2B+300-450=0
x%5E2+%2B+35x+-+150+=+0......use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-35+%2B-+sqrt%28+35%5E2-4%2A1%2A%28-150%29+%29%29%2F%282%2A1%29+

x+=+%28-35+%2B-+sqrt%28+1225%2B600+%29%29%2F2+

x+=+%28-35+%2B-+sqrt%28+1825+%29%29%2F2+

x+=+%28-35+%2B-+42.72%29%2F2+....find only positive root since width could be only positive number
x+=+%28-35+%2B+42.72%29%2F2+
x+=+7.72%2F2+
highlight%28x+=+3.86ft%29+

so, your answer is c. 3.860+ft