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

• A. $2:3:4$
• B. $6:4:3$
• C. $3:2:4$
• D. $3:2:1$

Answer 1

The correct option is B $6:4:3$

$Given:△ABC,AD,BEandCFarealtitudesdrawnonthesidesBC,CAandABrespectivelyAD:BE:CF=2:3:4LetAD=2x,BE=3x,CF=4xAreaof△ABC=\frac{1}{2}\times BC\times AD=\frac{1}{2}\times CA\times BE=\frac{1}{2}\times AB\times CF\Rightarrow BC\times AD=CA\times BE=AB\times CF\Rightarrow 2xBC=3xCA=4xAB\Rightarrow 2BC=3CA=4AB\Rightarrow \frac{BC}{6}=\frac{CA}{4}=\frac{AB}{3}\left[Dividingby12\right]\Rightarrow AB:BC:CA=6:4:3Henceoption\left(B\right)iscorrectanswer$