Question

The side lengths of a non-degenerate triangle $ABC$ are $4$,$11$ and $c$. The value of $c$ is

• A. $15$
• B. $7$
• C. $17$
• D. $12$

Answer 1

The correct option is D $12$

From the "Inequality of a triangle" property of a triangle, we know that the sum of any two sides of the triangle must be greater than the third side.

If $c=17$,
$11+4<17$ (not possible)

If $c=15$,
$11+4=15$ (not possible, a degenerate triangle is formed)

If $c=7$,
$11+4>7$
but, $7+4=11$(not possible, a degenerate triangle is formed)

$\therefore c=12$ as the sum of any two sided of the triangle will always be greater than the third side.