Question

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

$3.4cm,2.3cm,7.8cm$

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, taking any two sides of triangle at one time:

$$\begin{gathered} \Rightarrow 3.4cm+2.3cm=5.7cm<7.8cm \\ \Rightarrow 3.4cm+7.8cm=11.2cm>2.3cm \\ \Rightarrow 2.3cm+7.8cm=10.1cm>3.4cm \end{gathered}$$

Since, the sum of lengths of any two sides is not always greater than the third side, therefore triangle is not possible with these lengths as sides of the triangle.

Hence, the side lengths $3.4cm,2.3cm,7.8cm$ will not form a triangle.