SOLUTION: Find the dimensions of a rectangular Persian rug whose perimeter is 24 ft and whose area is 35f * t ^ 2

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Question 1153352: Find the dimensions of a rectangular Persian rug whose perimeter is 24 ft and whose area is 35f * t ^ 2
Answer by greenestamps(13203) About Me  (Show Source):
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Logically, with the rectangle having an area of 35 square feet, and with the perimeter and area both being whole numbers, the probable dimensions of the rug are 5 feet by 7 feet -- and those dimensions give the correct perimeter of 24 feet.

With formal algebra....

xy+=+35
2x%2B2y=24

Solve the second equation for either variable and substitute in the first equation:

x%2By+=+12
y+=+12-x
x%2812-x%29+=+35
12x-x%5E2+=+35
x%5E2-12x%2B35+=+0
%28x-7%29%28x-5%29+=+0
x+=+7 or x+=+5

The dimensions of the rug are x=7 and (12-x) = 5.