Question

prove that some of the altitudes of a triangle is less than sum of the 3 sides of a trianglre

Answer 1

given: AD BE CF are altitudes
to prove: AD+BE+CF<AC+BC+AB
proof:in triangle BCE,
angleBEC=90
Hence BC>BE(hyp is the longest side)
(1)

in triangleABD,angle ADB=90 HENCE AB>AD(hyp is the longest side)(2)

in triangleACF angle ACF=90 HENCE
AC>AF(hyp is the longest side)(3)


(1)+(2)+(3)

BC+AB+AC> BE +AD +CF
OR,
AD +BE+ CF <AB +BC +AC

HENCE PROVED!!!!