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Aman verma
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Geometry
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Source: Beat The GMAT — Problem Solving |
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theCodeToGMAT
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Is the answer [spoiler]{D}[/spoiler]?
Last edited by theCodeToGMAT on Sat Nov 16, 2013 12:05 pm, edited 1 time in total.
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Mathsbuddy
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Area of triangle = base x perpendicular height/2
We are given the ratios of the heights and are asked for the corresponding ratios of the bases.
So, area * 2 = AB * CD = AC * BF = CB * AE
Substituting the given ratios gives:
2AB = 3AC = 4BC
So AC = 2AB/3 AND BC = AB/2
this means that AB:AC:BC = AB:2AB/3:AB/2
Multiplying by 6 and dividing by AB gives the simplified ratio of 6:4:3
Hence the answer is (D) 6:4:3
We are given the ratios of the heights and are asked for the corresponding ratios of the bases.
So, area * 2 = AB * CD = AC * BF = CB * AE
Substituting the given ratios gives:
2AB = 3AC = 4BC
So AC = 2AB/3 AND BC = AB/2
this means that AB:AC:BC = AB:2AB/3:AB/2
Multiplying by 6 and dividing by AB gives the simplified ratio of 6:4:3
Hence the answer is (D) 6:4:3
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GMATGuruNY
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Any side of a triangle can be deemed the base.Aman verma wrote:
Q:In the given triangle ABC, CD,BF,and AE are the altitudes. If the ratio of CD:AE:BF=2:3:4 then the ratio of AB:BC:CA is:
(A) 4:3:2
(B) 2:3:4
(C) 4:9:6
(D) 6:4:3
(E) 5:2:1
Each base has a corresponding height.
Definition of height: the perpendicular distance between the base and the opposite vertex.
Let CD=2, AE=3, and BF=4.
Let the area = the LCM of 2, 3, and 4 = 12.
If AB is deemed the base, the corresponding height is CD.
Since the area = 12, we get:
(1/2)(AB)(CD) = 12
(1/2)(AB)(2) = 12
AB = 12.
If BC is deemed the base, the corresponding height is AE.
Since the area = 12, we get:
(1/2)(BC)(AE) = 12
(1/2)(BC)(3) = 12
BC = 8.
If AC is deemed the base, the corresponding height is BF:
Since the area = 12, we get:
(1/2)(AC)(BF) = 12
(1/2)(AC)(4) = 12
AC = 6.
Resulting ratio:
AB:BC:AC = 12:8:6 = 6:4:3.
The correct answer is D.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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