Question

In triangle abc,AE,BF,CDare the three altitudes in the ratio of CD:AE:BF=2:3:4 then the ratio of AB:BC:AC

Answer 1

Answer:

Given:△ABC,AD,BEandCFarealtitudesdrawnonthesidesBC,CAandABrespectively

AD:BE:CF=2:3:4

LetAD=2x,BE=3x,CF=4x

Areaof△ABC=

2

1

×BC×AD

=

2

1

×CA×BE

=

2

1

×AB×CF

⇒BC×AD=CA×BE=AB×CF

⇒2xBC=3xCA=4xAB

⇒2BC=3CA=4AB

⇒

6

BC

=

4

CA

=

3

AB

[Dividingby12]

⇒AB:BC:CA=6:4:3

Henceoption(B)iscorrectanswer