Question 1115552: The area of a rectangular wall of a barn is 80 square feet. Its length is 12 feet longer than twice its width? Found 2 solutions by stanbon, addingup:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The area of a rectangular wall of a barn is 80 square feet. Its length is 12 feet longer than twice its width? What are the dimensions?
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Width = W
Length = 2W+12
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Equation::
W(2W+12) = 80
2W^2 + 12W - 80 = 0
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W^2 + 6W - 40 = 0
(W+10)(W-4) = 0
Positive solution::
Width = 4 ft
Length = 2*4+12 = 20 ft
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Cheers,
Stan H.
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You can put this solution on YOUR website! width : W
length: L
L = W+12
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W x (W+12) = 80
W^2+12W = 80
The coefficient of W^1 is 1
The coefficient of 12W is 12, an even number
Thus, we'll complete the squares to solve.
Divide 12/2=6; square 6 and add to both sides:
W^2+12W+36 = 116 now we have a perfect square on the left.
Factor, remember that when x^2+bx+c is a perfect square you can factor it as (x+b/2)^2. So let's do it:
(W+6)^2 = 116
sqrt(W+6)^2 = sqrt116
x+6 = 2(sqrt29)-6 = 4.77
x+6 = -2(sqrt29)-6 = -16.77
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we are not looking for a negative number, so try 4.77:
4.77*(4.77+12) = 80 Correct, you have the correct answer.
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Happy learning,
John
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