gmat prep qn

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in the given figure, 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=

sq rt 2/2 s
sq rt 3/2 s
sq rt 2 s
sq rt 3 s
2s

[url=http://upload2.postimage.org/458724/photo_hosting.html][img]http://upload2.postimage.org/458724/untitled.jpg[/img][/url]
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Hi - if you do want us to answer this, please be sure to post an image file that works. :)

hi! i am stuck with this question as well but don't know how to post images :=( i cannot do any copying once i am in GMATPrep program. It doesn't even let me right click. can someone tell me how to do it? then i will post the figure for this problem.
thanks so much.

I don't know how to either! I've never posted an image! Can someone help our guest out?

Hi
You just have to do a print screen of the image. i.e. go to the GMATPrep Screen and on your keyboard press the Print Scr button, and then paste the given image in paint and save it as a .gif or .jpeg and voila u have ur image!!!
Hope it helps :)

I hope this can help..

Hi

It is clear that these are similar triangles - therefore their sides are proportionate/ of the same proportion

We know that the area of the bigger triangle is twice the are of the smaller one
Let us assume that S =4 and H =4 - the area of the bigger triangle is therefore S*H/2 =16/2 = 8

Therefore twice the area of the smaller triangle is 2(sh/2) =8 , sh =8

Since S=H, s=h and therefore 2s=8, s=2(2)^1/2

Therefore S/s= 4/2 SQRT 2 or
S =4s/2 sqrt 2 or sqrt 2 s

here's a nice takeaway for problems like this one.

in SIMILAR FIGURES, the RATIO OF AREAS is (RATIO OF LENGTHS)^2.

as long as we're at it:
in SIMILAR SOLIDS, the RATIO OF VOLUMES is (RATIO OF LENGTHS)^3.
in SIMILAR SOLIDS, the RATIO OF SURFACE AREAS is (RATIO OF LENGTHS)^2.

or, if you prefer your variables raw,
in similar figures:
length ratio = a : b
area ratio = a^2 : b^2

in similar 3-d solids:
length ratio = a : b
surface area ratio = a^2 : b^2
volume ratio = a^3 : b^3

in this problem, you have a^2 : b^2 = 2 : 1. if you know the result(s) above, then it follows at once that a : b (the ratio of lengths, which is what you're looking for) is √2 : 1.

good times!

notice that even if you're CLUELESS on this problem, you can still easily eliminate choices (a) and (b), each of which implies that the big "S" is actually smaller than the small "s". that is ridiculous.
this deduction follows from the fact that both √2/2 and √3/2 are less than 1. you should all know √2 ≈ 1.4 or 3/2, and √3 ≈ 1.7 or 7/4, so you should be able to figure this out.