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# Two isosceles Triangles have equal vertical angles and their

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Senior Manager
Joined: 03 Sep 2012
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Location: United States
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GMAT 1: 730 Q48 V42
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WE: Medicine and Health (Health Care)
Two isosceles Triangles have equal vertical angles and their [#permalink]

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15 Nov 2012, 07:39
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Question Stats:

80% (01:52) correct 20% (01:17) wrong based on 122 sessions

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Two isosceles Triangles have equal vertical angles and their areas are in the ratio 16:25. Find the ratio of their corresponding heights .

(A) 4/5

(B) 5/4

(C) 3/2

(D) 5/7

(E) 2/3
[Reveal] Spoiler: OA

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Joined: 02 Sep 2009
Posts: 39589
Re: Two isosceles Triangles have equal vertical angles and their [#permalink]

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15 Nov 2012, 07:59
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vomhorizon wrote:
Two isosceles Triangles have equal vertical angles and their areas are in the ratio 16:25. Find the ratio of their corresponding heights .

(A) 4/5

(B) 5/4

(C) 3/2

(D) 5/7

(E) 2/3

We are basically given that the triangles are similar.

In two similar triangles, the ratio of their areas is the square of the ratio of their sides and also, the square of the ratio of their corresponding heights.

Therefore, area/AREA=height^2/HEIGHT^2=16/25 --> height/HEIGHT=4/5.

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Re: Two isosceles Triangles have equal vertical angles and their [#permalink]

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15 Nov 2012, 08:23
Is there any other way to solve the problem in case you didn't know the formula of isosceles triangle = 1/2 (leg)^2
Senior Manager
Joined: 03 Sep 2012
Posts: 336
Location: United States
Concentration: Healthcare, Strategy
GMAT 1: 730 Q48 V42
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WE: Medicine and Health (Health Care)
Re: Two isosceles Triangles have equal vertical angles and their [#permalink]

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15 Nov 2012, 08:31
nelz007 wrote:
Is there any other way to solve the problem in case you didn't know the formula of isosceles triangle = 1/2 (leg)^2

This question trumped me the first time i attempted it, because SIMILARITY and properties of SIMILAR triangles are easy to forget, but they are very important, as i have seen quite a few questions where knowledge of similarity is important, especially when we have one big triangle being divided into two etc etc (MGMAT questions, in their advanced book) ..

In addition to the explanation given by Bunuel, this link is worth bookmarking :

http://www.mathopenref.com/similartriangles.html
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Re: Two isosceles Triangles have equal vertical angles and their [#permalink]

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16 Nov 2012, 18:30
nelz007 wrote:
Is there any other way to solve the problem in case you didn't know the formula of isosceles triangle = 1/2 (leg)^2

You can use the property of two similar triangles : If two similar triangles have corresponding side lengths in ratio a:b, then their areas will be in ratio a$$2$$ : b$$2$$
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Joined: 10 Oct 2012
Posts: 2
Concentration: Finance, Economics
Re: Two isosceles Triangles have equal vertical angles and their [#permalink]

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19 Aug 2013, 07:11
I have similar solution:

Area1: 16=1/2*a*h => a=32/h
Area2: 25=1/2*A*H => A=50/H

Find: h/H

Similar triangles so: h/H=a/A

Solve:

h/H=a/A

h/H=(32/h)/(50/H)

h/H=(32/h)*(H/50)

h/H=(32/50)*(H/h)

h/H=(16/25)*(H/h)

h^2/H^2=16/25

h/H=4/5

Answ: A.
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Re: Two isosceles Triangles have equal vertical angles and their [#permalink]

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25 Sep 2014, 11:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Two isosceles Triangles have equal vertical angles and their   [#permalink] 25 Sep 2014, 11:19
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