Question 671107: a rectangular flower garden has a length that is 7 feet less than twice its width. a 5-foot brick border is added around the garden and the area of the garden and the brick border is a total of 240 square feet. what are the dimmensioins of the garden without the brick border?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! L = length
W = width
length is 7 feet less than twice the width
L = 2W - 7
the brick border around the garden adds 10 to the length and 10 to the width (2 times 5 for each 1 because the border is on both side of the length and on both sides of the width).
the area with the border is equal to 240.
area = (L+10) * (W + 10) = 240
since L = 2W - 7, replace L with 2W - 7 to get:
area = (2W - 7 + 10) * (W + 10) = 240
simplify to get:
(2W + 3) * (W + 10) = 240
simplify by performing the indicated operations to get:
2W^2 + 23W + 30 = 240
subtract 240 from both sides to get:
2W^2 + 23W - 210 = 0
factor to get:
(2W + 35) * (W - 6) = 0
solve for W to get:
W = -35/2
W = 6
W can't be negative so you get W = 6 as the solution to the quadratic equation.
since L = 2W - 7, this means that:
L = 2(6) - 7 = 5
you have:
L = 5
W = 6
add 10 to both of these to include the border to get:
L + 10 = 15
W + 10 = 16
area = (L + 10) * (W + 10) = 15 * 16 = 240
area checks out ok.
L = 2W - 7 becomes 5 = 2(6) - 7 which becomes 12 - 7 which becomes 5 checks out as well since L does equal 5.
answer is confirmed as good.
answer is:
L = 5
W = 6
those are the dimensions of the garden without the brick border.
area of the garden without the brick border is equal to 5*7 = 35 square feet.
you weren't asked that, however, so you would not include it as part of your answer.
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