Question 836332: The perimeter, P, of a rectangular concrete slab is 46 m and it's area, A, is 90 m^2. Use the formula P + 2l + 2w. Determine the dimensions of the slab. Show your work.
I have tried to do this and keep getting the most ridiculous answers. This question has really stumped me and I have come to a stand still.
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! A = LW ... area of rectangle
90 = LW
LW = 90
L = 90/W
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P = 2L + 2W
46 = 2L + 2W
46 = 2(90/W) + 2W
46 = 180/W + 2W
W*(46) = W(180/W + 2W) ... Multiply both sides by W so we can clear out that fraction.
W*(46) = W(180/W) + W(2W)
46W = 180 + 2W^2
0 = 180 + 2W^2 - 46W
2W^2 - 46W + 180 = 0
2(W^2 - 23W + 90) = 0
W^2 - 23W + 90 = 0/2
W^2 - 23W + 90 = 0
(W - 18)(W - 5) = 0
W - 18 = 0 or W - 5 = 0
W = 18 or W = 5
if the width is W = 18, then the length is L = 90/W = 90/18 = 5.
if the width is W = 5, then the length is L = 90/W = 90/5 = 18.
So regardless of which value you pick for W, the other value for L will be the other solution.
In essence, the dimensions are 18 meters by 5 meters
Check:
A = LW = 18*5 = 90 square meters ... area checks out
P = 2L + 2W = 2*18 + 2*5 = 36+10 = 46 meters ... perimeter checks out
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