Question

If $(x+2),3,5$ are the lengths of sides of a triangle, then $x$ lies in

• A. $(0,6)$
• B. $(-4,6)$
• C. $(-1,6)$
• D. $(1,6)$

Answer 1

The correct option is A $(0,6)$

We know that the sum of any two sides of a triangle is always greater than the third side.
$\text{I}.(x+2)+3>5$
$\Rightarrow x>0$

$\text{II}.(x+2)+5>3$
$\Rightarrow x>-4$

$\text{III}.3+5>(x+2)$
$\Rightarrow x<6$

Taking intersection of the three cases, we get
$x\in (0,6)$