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

Helpful Geometry formula sheet:best-geometry-93676.html I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.

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

Re: Square region PRTV [#permalink]
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 \(XSTU=ST^2=(9-RS)^2\);

Or: as the ratio of the areas of squares is the square of the ratio of their sides then \(\frac{ST}{RS}=\frac{9-RS}{RS}=\frac{1}{2}\) --> \(RS=6\). _________________

Re: Square region PRTV [#permalink]
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: Square region PRTV [#permalink]
21 Nov 2013, 15:43

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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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