question_answer

The perimeter of a triangle is

A)  greater than the sum of its altitudes  

B)  less than the sum of its altitudes

C)  equal to the sum of its altitudes

D)  none of these

Correct Answer: A

Solution :

  In  \[\Delta ADC\] \[\angle D\,\,>\,\,\angle C\]                 \[\therefore \]  \[AC>AD\] Similarly \[AB>AD\] \[\therefore \] \[(AB+AC0>\,2AD\]                 \[(AB+BC)>\,2BE\] and        \[(AC+BC)>2CF\] \[\therefore \]  \[2(AB+BC+CA)>\,2(AD+BE+CF)\] \[\therefore \] \[(AB+BC+CA)\,>\,(AD+BE+CF)\]