Question

Among the following a true statement in ΔABC is

A)  \(\overline{AB}\) + \(\overline{BC}\) < \(\overline{AC}\)

B) \(\overline{BC}\) + \(\overline{CA}\) < \(\overline{AB}\)

C) \(\overline{AC}\) + \(\overline{AB}\)  > \(\overline{BC}\)

D) \(\overline{AB}\) + \(\overline{BC}\) = \(\overline{AC}\)

Answer 1

Correct option is (C) \(\overline{AC}+\overline{AB}>\overline{BC}\)

Since, sum of two sides in a triangle is always greater than the third side.

\(\therefore\) In \(\triangle ABC\)

\(\overline{AB}+\overline{BC}>\overline{AC},\)

\(\overline{AC}+\overline{BC}>\overline{AB}\) and

\(\overline{AB}+\overline{AC}>\overline{BC}\)

Hence, among all given options, only option (C) is correct.

Answer 2

 C) \(\overline{AC}\) + \(\overline{AB}\)  > \(\overline{BC}\)