Question

State which of the following sets of side lengths will form a triangle?

$2cm,3cm,4cm$.

Answer 1

Check if the given side lengths can form a triangle:

According to “Triangles Inequality”, the sum of the lengths of any two sides of a triangle must be greater than the third side.

Now,

$\Rightarrow 2cm+3cm=5cm>4cm$

$\Rightarrow 2cm+4cm=6cm>3cm$

$\Rightarrow 3cm+4cm=7cm>2cm$

Since, the sum of lengths of any two sides is greater than the third side, therefore triangle is possible with these lengths as side of triangle.

Hence, the side lengths $2cm,3cm,4cm$ will form a triangle.