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
Any side of a triangle can be deemed the
base.
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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