SOLUTION: find the dimensions of a rectangle with an area of 60ft^2 and a diagonal of 13ft

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Question 272079: find the dimensions of a rectangle with an area of 60ft^2 and a diagonal of 13ft
Answer by checkley77(12844) About Me  (Show Source):
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XY=60 OR X=60/Y
X^2+Y^2=13^2
(60/Y)^2+Y^2=169
3600/Y^2+Y^2=169
(3600+Y^4)/Y^2=169
3600+Y^4=169Y^2
Y^4-169Y^2+3600=0
(Y^2-144)(Y^2-25)=0
(Y+12)(Y-12)(Y+5)(Y-5)=0
Y-12=0
Y=12 ANS.
X=60/12=5 ANS.
Y-5=0
Y=5 ANS.
X=60/5=12 ANS.
PROOF
12*5=60
12^2+5^2=169
144+25=169
169=159