SOLUTION: .the area of a square bookcase is 21 more than the perimeter. find the length of a side

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Question 63560: .the area of a square bookcase is 21 more than the perimeter. find the length of a side
Answer by joyofmath(189) About Me  (Show Source):
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.the area of a square bookcase is 21 more than the perimeter. find the length of a side
Let L = the side of the bookcase.
Let P = the perimeter of the bookcase.
Let A = the area of the bookcase.
Then, we know that:
A=P%2B21
A=L%5E2
P=4L
So, A=L%5E2=P%2B21.
But, P=4L so A=L%5E2=4L%2B21.
So, L%5E2+=+4L%2B21.
Or, L%5E2-4L-21=0.
This factors to %28L%2B3%29%28L-7%29=0.
So, L=-3 or L=7.
The length can't be negative so L=7.
Let's verify the answer.
If L=7 then P=4%2A7=28 and A=L%5E2=7%5E2=49.
So, A is indeed 21 more than P.