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In the figure above, the area of square region PRTV is 81, a

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In the figure above, the area of square region PRTV is 81, a [#permalink] New post 09 Nov 2010, 00:08
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In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS?

A. 5
B. 5.5
C. 6
D. 6.5
E. 7
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Nov 2013, 00:28, edited 1 time in total.
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Re: Square region PRTV [#permalink] New post 09 Nov 2010, 00:17
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In the figure above, the area of square region PRTV is 81, and the ratio of the area of square region XSTU to the area of square region PQXW is 1 to 4. What is the length of segment RS?
A. 5
B. 5.5
C. 6
D. 6.5
E. 7

As the area of square region PRTV is 81 then \(RT^2=81\) --> \(RT=9\);

The area of square region \(PQXW=QX^2=RS^2\) and the area of square region \(XSTU=ST^2=(9-RS)^2\);

Given: \(\frac{(9-RS)^2}{RS^2}=\frac{1}{4}\) --> \(\frac{9-RS}{RS}=\frac{1}{2}\) --> \(RS=6\).

Answer: C.

Or: as the ratio of the areas of squares is the square of the ratio of their sides then \(\frac{ST}{RS}=\frac{9-RS}{RS}=\frac{1}{2}\) --> \(RS=6\).
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Re: Square region PRTV [#permalink] New post 09 Nov 2010, 02:22
(ST)^2/(QX)^2 = 1/4
So, QX=RS=2ST
since- RT=9(total area of PRTV=81), RT= 3ST.
So ST=3 and RS=6

Answer: C
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Re: Square region PRTV [#permalink] New post 09 Nov 2010, 07:16
answer is 6
If the area is 1:4 than the sides will be 1:2
since the total length is 9 (RS+ST) hence it is (3+6) since RS is the Bigger in length therefore,RS = 6
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Re: Geometry ratio [#permalink] New post 05 Jan 2011, 21:51
I don't agree with the answer "D" - I think it's C

PRTV is a square, with area of 81 => RT = 9

RT = RS + ST = 9

RS^2 = 4ST ^ 2
=> RS = 2ST

=>3ST = 9
=> ST = 3

=> RS = 6

Answer: C
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Re: Geometry ratio [#permalink] New post 05 Jan 2011, 23:33
RT=9 since area of square is 81

Let RS=x and ST=9-x

Ratio of the area of squares is 1:4
Hence x^2 = 4 (9-x)^2
Hence x = 2(9-x)
3x = 18 ... x=6

ANswer is (c)
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Re: Square region PRTV [#permalink] New post 21 Nov 2013, 15:43
Hello from the GMAT Club BumpBot!

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Re: In the figure above, the area of square region PRTV is 81, a [#permalink] New post 07 Feb 2015, 05:59
Hello from the GMAT Club BumpBot!

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Re: In the figure above, the area of square region PRTV is 81, a   [#permalink] 07 Feb 2015, 05:59
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