SOLUTION: The area of the rectangle is 100 square cm. If a square built using a diagonal of this rectangle as one of its sides, the square has area 700 square cm. What is the perimeter of

Question 320726: The area of the rectangle is 100 square cm. If a square built using a diagonal of this rectangle as one of its sides, the square has area 700 square cm. What is the perimeter of the rectangle?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
The area of the rectangle is 100 square cm. If a square built using a diagonal of this rectangle as one of its sides, the square has area 700 square cm. What is the perimeter of the rectangle?
let length be x
width be y
xy=100
..
the diagonal of the rectangle = sqrt(x^2+y^2)
this is the side of the square
Area of this square = sqrt(x^2+y^2)*sqrt(x^2+y^2)
= x^2+y^2
..
x^2+y^2=700
x^2+2xY+y^2= 700+2xy
(x+y)^2= 700+200
(x+y)^2= 900
(x+y)= 30
(x+100/x)=30
x^2+100 /x =30
x^2+100=30x
x^2-30x+100=0
The roots of the equation x1 , x2
x1= 30 +sqrt(900-400) /2
x1=26.18 cm
x2= 30 -sqrt(900-400) /2
x2=3.82 cm
..
perimeter of rectangle = (2*3.82)+(2*25.18)
=60 cm
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