question_answer

Which of the following statements is TRUE?

Statement 1: The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Statement 2: If P is a point on the side BC of \[\Delta ABC\]. Then \[(AB+BC+AC)>2AP\]

A)  Only Statement-1

B)  Only Statement-2

C)  Both Statement-1 and Statement-2

D)  Neither Statement-1 nor Statement-2

Correct Answer: C

Solution :

Statement - 2               In  \[\Delta ABP,~\] \[AB+BP>AP~\]       ?..(i)      In  \[\Delta APC\] \[PC+AC>AP\]          ?..(ii) Adding (i) & (ii), we get \[AB+BP+PC+AC>AP+AP\] \[\Rightarrow \]  \[AB+BC+AC>2AP\] \[\therefore \] Both Statement -1 and Statement-2 are true.