SOLUTION: A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of

Question 787145: A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of uniform width around the garden. If the border is to have a depth of 3 inches, how wide will the border be?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A landscaper, who just completed a rectangular flower garden measuring 6 feet by 10 feet, orders 1 cubic yard of premixed cement, all of which is to be used to create a border of uniform width around the garden.
If the border is to have a depth of 3 inches, how wide will the border be?
:
Find the area which can be covered with 3" of concrete, in square feet:
1 cu/yd = 27 cu/ft
3" = 1/4 or .25 ft
:
= 108 sq/ft is the border area covered by concrete
:
Let x = the width of the border, then the overall dimensions will be:
(2x+6) by (2x+10)
:
Overall area - garden dimension area = border area
(2x+6)(2x+10) - (6*10) = 108
FOIL
4x^2 + 20x + 12x + 60 - 60 = 108
combine as a quadratic equation
4x^2 + 32x - 108 = 0
simplify, divide by 4
x^2 + 8x - 27 = 0
You will have to use the quadratic formula to find x
I got a positive solution of 2.5574 ft as the width of border (about 2' 7")
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