SOLUTION: The perimeter of a rectangle is 114m, and the area of the rectangle is 56m^2. Find the dimension of the rectangle.

Algebra ->  Rectangles -> SOLUTION: The perimeter of a rectangle is 114m, and the area of the rectangle is 56m^2. Find the dimension of the rectangle.      Log On


   

Question 665644: The perimeter of a rectangle is 114m, and the area of the rectangle is 56m^2. Find the dimension of the rectangle.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Given
p = 114 = 2l + 2w
a = 56 = (l)(w), which is the same as l = 56%2Fw
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Substitute the second equation into the first
256%2Fw + 2w = 114
112%2Fw + 2w = 114
Multiply the entire equation by w
112 + 2w%5E2 = 114w
2w%5E2 - 114w + 112 = 0
Factor
(2w-112)(w-1)
2w-112=0, so w = 56
w-1=0, so w=1
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Dimensions are highlight%2856%29m by highlight%281%29m
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Check cartoon%28%0D%0Aa+=+%2856%29%281%29%2C%0D%0Aa+=+56%29
cartoon%28%0D%0Ap+=+2%281%29+%2B+2%2856%29%2C%0D%0Ap+=+2+%2B+112%2C%0D%0Ap+=+114%29
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