Gmat prep similar triangles

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vkb16: Master | Next Rank: 500 Posts; Posts: 122; Joined: Mon Dec 15, 2008 12:03 am; Thanked: 2 times

by vkb16 » Mon May 04, 2009 10:35 pm

OA is C

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Source: Beat The GMAT — Problem Solving | Mon May 04, 2009 10:35 pm

bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

by bluementor » Tue May 05, 2009 12:31 am

Lets say:

height of small triangle = h
height of big triangle = H

we know that:
base of small triangle = s
base of big triangle = S

Area of big triangle = 2 x Area of small triangle
(1/2)*H*S = 2*(1/2)*h*s

Since both triangles are similar (their internal angles are identical), the ratio of the corresponding lengths must be equal:

s/S = h/H

So,

(1/2)*H*S = 2*(1/2)*h*s
H*S = 2*h*s
S = 2*s*(h/H)
S = 2*s*(s/S)
S^2 = 2*(s^2)
S = (√2)*s

Choose C.

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Pranay: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Tue May 05, 2009 1:58 am; Thanked: 1 times

by Pranay » Tue May 05, 2009 2:17 am

bluementor wrote:Lets say:

height of small triangle = h
height of big triangle = H

we know that:
base of small triangle = s
base of big triangle = S

Area of big triangle = 2 x Area of small triangle
(1/2)*H*S = 2*(1/2)*h*s

Since both triangles are similar (their internal angles are identical), the ratio of the corresponding lengths must be equal:

s/S = h/H

So,

(1/2)*H*S = 2*(1/2)*h*s
H*S = 2*h*s
S = 2*s*(h/H)
S = 2*s*(s/S)
S^2 = 2*(s^2)
S = (√2)*s

Choose C.

-BM-

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