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Simple Geometry Problem GMAT Prep

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Simple Geometry Problem GMAT Prep [#permalink] New post 14 Jan 2009, 02:18
can someone give me an explanantion? Don't get it :oops:
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Re: Simple Geometry Problem GMAT Prep [#permalink] New post 14 Jan 2009, 08:37
since angles are same, so the triangles are similar. for similar triangles, the ratio of areas= square of the ratio of similar sides. So if the areas r in ratio 2:1, then the sides are in ratio sqrt(2):1.
Hence C
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Re: Simple Geometry Problem GMAT Prep [#permalink] New post 16 Jan 2009, 13:03
base of the small triangle = s
base of the large triangle = S

height of the small triangle = h
height of the large triangle = H

since corrosponding angtles are equal, the traingles are similar. so ---->
s/S = h/H
Hs= hS
H = hS/s

area of the small triangle = a = 1/2 (hs)
area of the large triangle = 1/2 (HS)

area of the large triangle = 2 (area of the small triangle)
1/2 (HS) = 2 [1/2 (hs)]
(hS/s)(S) = 2hs
S^2 = 2s^2
S = s(sqrt2) or sqrt2(s)
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Re: Simple Geometry Problem GMAT Prep [#permalink] New post 17 Jan 2009, 18:50
Let the height of small triangle be h and the second triangle be H.
Given two triangles are similar ...so the sides are proportional
so

S/s = H/h
Sh/s = H

Given area of the second triangle is twice the area of the first triangle

1/2 S H = 2 . 1/2 . s h

!/2 SH = sh

plug in H as Sh/s

1/2 S. Sh/s = sh

1/2 S^2 = s^2

S^2 = 2 s^2

S = sqrt 2 S


answer C.

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Re: Simple Geometry Problem GMAT Prep [#permalink] New post 17 Jan 2009, 18:51
Let the height of small triangle be h and the second triangle be H.
Given two triangles are similar ...so the sides are proportional
so

S/s = H/h
Sh/s = H

Given area of the second triangle is twice the area of the first triangle

1/2 S H = 2 . 1/2 . s h

!/2 SH = sh

plug in H as Sh/s

1/2 S. Sh/s = sh

1/2 S^2 = s^2

S^2 = 2 s^2

S = sqrt 2 S


answer C.

http://www.graduatetutor.com
Re: Simple Geometry Problem GMAT Prep   [#permalink] 17 Jan 2009, 18:51
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