SOLUTION: The perimeter of a rectangle is 34 feet, and the diagonal is 13 feet long. What are the length and width of the rectangle?

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Question 6680: The perimeter of a rectangle is 34 feet, and the diagonal is 13 feet long. What are the length and width of the rectangle?
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
let the length be x feet
let the width be y feet


P=2(x+y)=34 feet
(x+y)=17


diagonal=13 feet
(13)^2=x^2+y^2
169=[(x+y)^2]-2xy
169=[(17)^2]-2xy
169-289=-2xy
xy=120/2
xy=60


x+y=17
xy=60
Then,x=17-y
xy=60
(17-y)y=60
-y^2+17y-60=0
-y^2+5y+12y-60=0
y(-y+5)-12(-y+5)=0
(-y+5)(y-12)=0
y=5 or 12


xy=60,y=5 or 12
therefore,x=12 or 5


{x,y} = {5,12} OR {12,5}

Prabhat.