SOLUTION: A rectangle has an area of 96 square centimeters and a perimeter of 40 centimeters. What are the dimensions of the rectangle? And how do I show my work?

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Question 305493: A rectangle has an area of 96 square centimeters and a perimeter of 40 centimeters. What are the dimensions of the rectangle? And how do I show my work?
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
XY=96
X=96/Y
2X+2Y=40
2(96/Y)+2Y=40
192/Y+2Y=40
(192+2Y^2)/Y=40
2Y^2+192=Y*40
2Y^2+192=40Y
2Y^2-40Y+192=0
2(Y^2-20Y+96)=0
2(Y-8)(Y-12)=0
Y-8=0
Y=8 ANS.
X*8=96
X=96/8
X=12 ANS.
PROOF:
8*12=96
2*8=2*12=40
16+24=40
40=40