Question

D is a point on the side of the BC of ΔABC. Prove that the perimeter of ΔABC is greater than twice of AD.

Answer 1

Construction: Join AD
In triangle ACD,
AC + CD > AD  ...(i)
(Sum of two of a triangle greater than the third side)
Similarly, in triangle ADB,
AB + BD > AD  ...(ii)
Adding (i) and  (ii),
AC + CD + AB + BD > AD
AB + BC + AC > 2AD.   ...(Since, CD + BD = BC)