Question

prove that the perimetreof a triangle is greater than the sum of all three medians

Answer 1

LET ABC BE TRIANGLE WITH MEDIANS AD,BE AND CF

THE SUM OF TWO SIDES OF A TRIANGLE IS MORE THAN TWICE THE MEDIAN BISECTING THIRD SIDE.

LET AD BE THE MEDIAN TO BC,BE TO AC AND CF TO AB,

THEN AB+AC>2AD--------1

BC+AB>2BE-----------------2

AC+BC>2CF------------------3

ADDING 1,2,3

2(AB+BC+AC)>2(AD+BE+CF)

AB+BC+AC>AD+BE+CF

REMEMBER ALWAYS TO WRITE IN FORMAT FOR PROVING A PROBLEM