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If 3/5 of a circular floor is covered by a rectangular rug t

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If 3/5 of a circular floor is covered by a rectangular rug t [#permalink] New post 27 Jun 2018, 09:23
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If \(\frac{3}{5}\) of a circular floor is covered by a rectangular rug that is \(x\) feet by \(y\) feet, which of the following represents the distance from the center of the floor to the edge of the floor?

A. \(\frac{5 \sqrt{xy}}{3\pi}\)

B. \(\sqrt{\frac{5xy}{3 \pi}}\)

C. \(\frac{3\pi}{ 5 \sqrt{xy}}\)

D. \(\sqrt{xy}\) \(- \frac{3 \pi}{5}\)

E. \(\sqrt{\frac{3xy}{5\pi}}\)
[Reveal] Spoiler: OA

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Re: If 3/5 of a circular floor is covered by a rectangular rug t [#permalink] New post 28 Jun 2018, 11:45
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Carcass wrote:
If \(\frac{3}{5}\) of a circular floor is covered by a rectangular rug that is \(x\) feet by \(y\) feet, which of the following represents the distance from the center of the floor to the edge of the floor?

A. \(\frac{5 \sqrt{xy}}{3\pi}\)

B. \(\sqrt{\frac{5xy}{3 \pi}}\)

C. \(\frac{3\pi}{ 5 \sqrt{xy}}\)

D. \(\sqrt{xy}\) \(- \frac{3 \pi}{5}\)

E. \(\sqrt{\frac{3xy}{5\pi}}\)


Without a diagram took me 3:45 mins time to solve this and unnecessarily started to draw vague diagram. Later realized the solution properly.

Follow the below diagram.

When it is mentioned that 3/5 circle area that means out of 5 parts 3 parts area is equal to rectangle area.

i.e. xy (area of rectangle) = 3/5 ( pi * r^2 ) .

=> \(\sqrt{\frac{5xy}{3 \pi}}\).
Attachments

cir.PNG
cir.PNG [ 17.95 KiB | Viewed 225 times ]

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Re: If 3/5 of a circular floor is covered by a rectangular rug t [#permalink] New post 28 Jun 2018, 12:16
Carcass wrote:
If \(\frac{3}{5}\) of a circular floor is covered by a rectangular rug that is \(x\) feet by \(y\) feet, which of the following represents the distance from the center of the floor to the edge of the floor?

A. \(\frac{5 \sqrt{xy}}{3\pi}\)

B. \(\sqrt{\frac{5xy}{3 \pi}}\)

C. \(\frac{3\pi}{ 5 \sqrt{xy}}\)

D. \(\sqrt{xy}\) \(- \frac{3 \pi}{5}\)

E. \(\sqrt{\frac{3xy}{5\pi}}\)


Here,
We need to find out the radius of the circle
From the ques we know

\(\frac{3}{5}\) of the circle area = area of the rectangle

or \(\frac{3}{5}\) * area of the circle = area of rectangle

or \(\frac{3}{5} * \pi * r^2\)= x * y

or \(r^2\) = \(\frac{5xy}{3 \pi}\)

or r = \(\sqrt{\frac{5xy}{3 \pi}}\)
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Re: If 3/5 of a circular floor is covered by a rectangular rug t   [#permalink] 28 Jun 2018, 12:16
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