Question 1082711: A landscaper who just completed a rectangular flower garden measuring 13 feet in length by 6 feet in width, orders 1 cubic yard of premixed cement, all of which is to be used to create a boarder of uniform width around the garden of the boarder is to have a depth of 4 inches how wide will the boarder be?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It helps to draw this.
The border+garden is (13+2x)*(6+2x)=4x^2+38x+78
subtract the garden's area, which is 78,
border is 4x^2+38x ft^2.
the depth is 1/3 of a foot.
The volume of the border is (1/3)(4x^2+38x) ft^3
That will be filled with 27 ft^3 (3ft)^3 of cement
Therefore, (1/3)(4x^2+38x)=27
4x^2+38x=81, multiplying by 3
4x^2+38x-81=0
x=(1/8)(-38+/- sqrt (1444+1296)); sqrt(2740)=52.35
x=(14.35/8)=1.79 feet
Check using 2 feet wide
That makes the garden+border 10*17=170 ft^2
The border is 170-78=92 ft^2
4 inches deep is 1/3 of a foot, and that is 30 2/3 ft^3, which is a little more than a cubic yard, as it should be.
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