Question

If the altitudes of a triangle are in the ratio 2 : 3 : 4, then the lengths of the corresponding sides are in the ratio

Answer 1

Solution :-

Let ABC be the triangle and AB, BC And CD be the sides and CD, BF and AE be the altitudes. 

Given - Altitudes are in the ratio 2 : 3 : 4

Let CD = 2, BF = 3 and AE = 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 is 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 is 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 is 12, we get :

(1/2) (AC) (BF) = 12

(1/2) (AC) (4) = 12

AC = 6

SO, the ratio of three sides is  

12 :  8 : 6

= 6 : 4 : 3

Answer.

Answer 2

hey mate, here is your answer...

:-)

let CD be 2, AE be 3 and BF be 4.

LCM of 2,3,4 is 12

ar(∆ABC) = 12

CD×AB =12

2×AB=12

AB=6

similarly,

BC =4

and,

CA=3

Now,

AB:BC:CA = 6:4:3