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Rectangle ABCD is inscribed in circle C. What is the

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Rectangle ABCD is inscribed in circle C. What is the [#permalink] New post 25 Jun 2008, 02:46
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Rectangle ABCD is inscribed in circle C. What is the perimeter of the rectangle?
1. The area of the circle C is 78.5
2. The length and width of the rectangle are in the ratio of 4 to 3.
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Re: DS: perimeter of the rectangle [#permalink] New post 25 Jun 2008, 03:09
(1) is insufficient since in a given circle you can inscribe a lot of different rectangles

(2) is insufficient since you miss the size of the circle (a proportion alone doesn't give you lengths)

(1) and (2) are sufficient: in a given circle there is just one shape (and many orientations) that fit the ratio 4:3

--> Answer is (C)
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Re: DS: perimeter of the rectangle [#permalink] New post 25 Jun 2008, 03:32
C for me as well.

From 1, you only know the radius/diameter of the circle, which only gives you one side of the rectangle. insuff.

From 2, the sides could take on many different values, since all we know is a ratio. insuff.

Together, from 1 we can find the radius and diameter, which gives us the length of the rectangle, and then using the ratio, we can find the width. Sufficient.
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Re: DS: perimeter of the rectangle [#permalink] New post 25 Jun 2008, 03:34
pmenon wrote:
C for me as well.

From 1, you only know the radius/diameter of the circle, which only gives you one side of the rectangle. insuff.

From 2, the sides could take on many different values, since all we know is a ratio. insuff.

Together, from 1 we can find the radius and diameter, which gives us the length of the rectangle, and then using the ratio, we can find the width. Sufficient.

I don't think that knowing the radius/diameter of the circle gives one side of the rectangle.

Else: what would be this side for a circle of diameter 10cm ?
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Re: DS: perimeter of the rectangle [#permalink] New post 25 Jun 2008, 03:57
my mistake, i had thought that since the rectangle was inscribed inside the circle, the the length of the rectangle would equal the diameter of the circle
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Re: DS: perimeter of the rectangle [#permalink] New post 26 Jun 2008, 01:03
ritula wrote:
Rectangle ABCD is inscribed in circle C. What is the perimeter of the rectangle?
1. The area of the circle C is 78.5
2. The length and width of the rectangle are in the ratio of 4 to 3.

Given:
the diagonal of the inscribed rectangle will be diameter of the circle

1) we can calculate radius, insuff
2) we know the ratio l/w=4/3 or l = 4/3*w, insuff alone

together
(2r)^2 = l^2 + w^2 = (4/3*w)^2 + (w)^2 , r is known from (1) so w and then l can be calculated
Re: DS: perimeter of the rectangle   [#permalink] 26 Jun 2008, 01:03
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