Question

Perimeter of triangle is greater than the sum of its altitudes

Answer 1

Given: ΔABC in which AD⊥BC, BE⊥AC and CF⊥AB To prove: AD + BE + CF < AB + BC + AC Figure: Proof: We know that of all the segments that can be drawn to a given line, from a point not lying on it, the perpendicular distance i.e., the perpendicular line segment is the shortest. Therefore, Adding (1), (2) and (3), we get AB+AC+BA+BC+CA+CB>2AD+2BE+2CF ⇒ 2AB+2BC+2CA>2(AD+BE+CF) ⇒ 2(AB+BC+CA)>2(AD+BE+CF) ⇒ AB+BC+CA>AD+BE+CF ⇒ The perimeter of the triangle is greater than the sum of its altitudes Therefore, Hence proved

hope its help you

nice to hepl you

please mark it as brainlist

and follow me

thanks a lot