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In the figures above, if the area of the triangle on the right is twic [#permalink]
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08 Mar 2010, 11:02
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In the figures above, if the area of the triangle on the right is twice the area of the triangle on the left, then in terms of s, S= A. \(\frac{\sqrt{2}}{2}s\) B. \(\frac{\sqrt{3}}{2}s\) C. \(\sqrt{2}s\) D. \(\sqrt{3}s\) E. \(2s\) OPEN DISCUSSION OF THIS QUESTION IS HERE: inthefiguresaboveiftheareaofthetriangleonthe128929.htmlAttachment:
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Re: In the figures above, if the area of the triangle on the right is twic [#permalink]
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08 Mar 2010, 13:02
seems easy enough....
for similar triangles (all angles the same) the following holds:
(area A)/(area b) = ( x/y )^2 (where x and y are corresponding lengths)
in this case, let A be the area of the smaller triangle. We have:
2A/A = (S/s)^2 => S/s = 2^0.5 S = s*2^0.5

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Re: In the figures above, if the area of the triangle on the right is twic [#permalink]
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08 Mar 2010, 13:18
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For Small triangle, lets say h is the height. And for the big triangle, H is the height. Area = 1/2 (s*h) Area = 1/2 (S*H) According to the info in the question > 1/2 (S*H) = 2 * [1/2 (s*h)] = s*h => s = S*H/2h => h/H = S/2s 1 For similar triangles h/H = s/S 2 put 2 in 1 ==> s/S = S/2s => s^2 = S^2/2 = sqrt(2).s = S So, sqrt(2) is your answer!
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Re: In the figures above, if the area of the triangle on the right is twic [#permalink]
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15 Mar 2010, 09:29
With the property ratio of area in similar triangle = (ratio of any similar side)^2 so s/S = sqrt(1/2) => S = s*sqrt(2) hence C is the answer
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Re: In the figures above, if the area of the triangle on the right is twic [#permalink]
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20 Mar 2010, 09:01
nickk wrote: seems easy enough....
for similar triangles (all angles the same) the following holds:
(area A)/(area b) = ( x/y )^2 (where x and y are corresponding lengths)
in this case, let A be the area of the smaller triangle. We have:
2A/A = (S/s)^2 => S/s = 2^0.5 S = s*2^0.5 Where does this property comes from??
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Re: In the figures above, if the area of the triangle on the right is twic [#permalink]
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21 Mar 2010, 12:10
mustdoit wrote: nickk wrote: seems easy enough....
for similar triangles (all angles the same) the following holds:
(area A)/(area b) = ( x/y )^2 (where x and y are corresponding lengths)
in this case, let A be the area of the smaller triangle. We have:
2A/A = (S/s)^2 => S/s = 2^0.5 S = s*2^0.5 Where does this property comes from?? This is the similar trianlges property. Any two triangles are similar if they have same corresponding angles or if the ratio of their corresponding sides are same. In case two triangles are similar, ratio of their areas = (ratio of side)^2
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GMAT PREP (PS) [#permalink]
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06 May 2010, 12:34
Please explain...
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Re: GMAT PREP (PS) [#permalink]
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06 May 2010, 13:05
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Re: GMAT PREP (PS) [#permalink]
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06 May 2010, 13:34
Bunuel wrote: LM wrote: Please explain... Property of similar triangles: In two similar triangles, the ratio of their areas is the square of the ratio of their sides. Hence \(\frac{AREA}{area}=\frac{S^2}{s^2}=2\) > \(S=s\sqrt{2}\). Answer: C. Thanks I did not know this! the ratio of their areas is the square of the ratio of their sides.

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Re: GMAT PREP (PS) [#permalink]
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25 Aug 2010, 02:24
Bunuel that was awesome...although read all concepts in your Polygon blog..but did not click to me. +1 to you as always
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Re: GMAT PREP (PS) [#permalink]
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08 Sep 2010, 06:39
This is certainly not a 700 Level question Bunuel can be moved

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Tough Geometry PS Help Please! [#permalink]
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06 Oct 2010, 06:29
I eliminated A and B for this because I knew that S had to be greater than s, but I did not know how to find the exact answer. I also eliminated 2s because that excludes the height when calculating area, but again I could not figure out how to get the exact answer. Any help please?? Thanks!!! The file is attached. Jeremiah

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Re: Tough Geometry PS Help Please! [#permalink]
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06 Oct 2010, 06:39

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Re: GMAT PREP (PS) [#permalink]
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23 Oct 2010, 10:08
If you don't know the property: take H=height of the larger triangle and h=height of the smaller triangle
As the area is twice ,so HS=2hs because triangles are similar h/s=H/S or h/H=s/S
Now after solving we get S=(2^1/2)s Answer: C.

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Re: In the figures above, if the area of the triangle on the right is twic [#permalink]
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Re: In the figures above, if the area of the triangle on the right is twic [#permalink]
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05 May 2016, 07:50

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Re: In the figures above, if the area of the triangle on the right is twic
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