Question

The side length of a $\Delta$ ABC are 4, 11 and $x$. Which of the following is a possible value of $x$?

• A. 12
• B. 15
• C. 17
• D. 7

Answer 1

The correct option is A 12

Suppose $x$ be the largest side in the triangle,
then $4+11>x$ $⟹$ $x<15$. --- (i)

Consider $x$ is the second largest side, then
$4+x>11$ $⟹$ $x>7$ ----(ii)

$x$ can not be the smallest side, because trinagle inequality not get valid in that situation. That is if $x<4$ , then $x+4$ can't be greater than 11.

So from (i) and (ii), 7< x <15. Hence, the possible value is 12.