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TAGS: Moderator  Joined: 18 Apr 2015
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If 3/5 of a circular floor is covered by a rectangular rug t [#permalink]
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Expert's post 00:00

Question Stats: 81% (01:27) correct 18% (02:43) wrong based on 11 sessions
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]
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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 [ 17.95 KiB | Viewed 334 times ]

Director Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Re: If 3/5 of a circular floor is covered by a rectangular rug t [#permalink]
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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