A rectangle has the area of 100 and one of its side is x. If its perimeter is equal to the circumference of a circle, in terms of x, what is the area of the circle?
i got an answer that is: [spoiler](100/x + x)^2[/spoiler]
OA is [spoiler](100/x + x)^2 / pi[/spoiler]
please lemme know whether u get my answer coz i doubt that OA is misprinted in the source.
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rectangle
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area of rectangle = 100
if one side is x --> the other side is 100/x
-> perimeter == 2 ( x + 100/x )
if (perimeter == circumference)
2 (x + 100/x) = 2 * pi * r
pi * r = (x + 100/x)
r = (x + 100/x) * 1/pi
Area of circle = pi * r^2
= pi * ((x + 100/x) * 1/pi ) ^ 2
= 1/pi (x + 100/x) ^ 2
if one side is x --> the other side is 100/x
-> perimeter == 2 ( x + 100/x )
if (perimeter == circumference)
2 (x + 100/x) = 2 * pi * r
pi * r = (x + 100/x)
r = (x + 100/x) * 1/pi
Area of circle = pi * r^2
= pi * ((x + 100/x) * 1/pi ) ^ 2
= 1/pi (x + 100/x) ^ 2
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scholardream
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I agree with the OA.
The another side is 100/x -> Perimeter of cycle is 2*Pi*r = (100/x+x)*2 -> r = (100/x+x)/Pi
Area of the cycle = Pi*r^2 = Pi*(100/x+x)^2/Pi^2 = (100/x+x)^2/Pi
The another side is 100/x -> Perimeter of cycle is 2*Pi*r = (100/x+x)*2 -> r = (100/x+x)/Pi
Area of the cycle = Pi*r^2 = Pi*(100/x+x)^2/Pi^2 = (100/x+x)^2/Pi
