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

Algebra ->  Rectangles -> SOLUTION: The area of a rectangle is 100 square cm. If a square is built using a diagonal of this rectangle as one of its sides, the square has area 700 square cm. What is the perimeter of t      Log On


   

Question 318499: The area of a rectangle is 100 square cm. If a square is 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?
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a rectangle is 100 square cm. If a square is 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?
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A side of the 2nd square is sqrt(700)
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Let a side of the 1st square be "x"
Equation:
x^2 + x^2 = (sqrt(700))^2
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2x^2 = 700
x^2 = 350
x = sqrt(350)
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Perimeter of the 1st square = 4*sqrt(350)
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Cheers,
Stan H.
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Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
length of rectangle= x
widthof rectangle =y
area = xy =100
..
diagonal = sqrt(x^2+y^2)
side of square = Sqrt(x^2+y^2)
Area =sqrt(x^2+y^2)*sqrt(x^2+y^2)
x^2+y^2=700
add 2xy to both sides
x^2+2xy+y^2=700+2xy
(x+y)^2=700+2xy
(x+y)^2=700+200
(x+y)^2=900
x+y=30
Perimeter = 2(x+y)
perimeter = 2*30=60 sq.cm