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In the figure above, the area of square region PRTV is 81, a [#permalink]

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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?

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Last edited by Bunuel on 22 Nov 2013, 00:28, edited 1 time in total.

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 \(XSTU=ST^2=(9-RS)^2\);

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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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: In the figure above, the area of square region PRTV is 81, a [#permalink]

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07 Feb 2015, 05:59

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Re: In the figure above, the area of square region PRTV is 81, a [#permalink]

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17 Sep 2016, 05:45

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