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?

Question 353659: 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 sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!
Let length is 'a' and width is 'b'.
according to question,
perimeter 2(a+b)= 34

or, a+b = 17 ...........(1)

a^2 + b^2 = (13)^2

=> a^2 + b^2 = 169

now putting a = 17-b from (1) in above equation
=> (17-b)^2 + b^2 = 169

=> 289 + b^2 - 34b + b^2 = 169

=> 2b^2 -34b + 120 = 0

=> b^2 - 17b + 60 = 0 (dividing by 2)

=> b^2 -12b -5b +60 =0

=> b(b-12)-5(b -12) = 0

=> ( b-5) (b-12) = 0

so, b= 5 or b =12

if b= 5, a = 12

if b = 12 , a= 5

so length and width are 5 and 12.
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