Question

Using triangle inequality theorem check whether the given side lengths $a=3,b=5$ and $c=1$ will form a triangle or not.

Answer 1

According to the triangle inequality theorem the sum of any two side of the triangle must be greater than the measure of the third side.

$A+B>C$

$B+C>A$

$A+C>B$

Here $A=3,B=5$ and $C=1$

$\Rightarrow 3+5>1$

$\Rightarrow 5+1>3$

$\Rightarrow 3+1<5$

$\therefore$ third condition is not satisfied according to the theorem, then the given side length will not form a triangle.