Question

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

$4mm,19mm,12mm$

Answer 1

Check if 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 triangles at one time:

$$\begin{gathered} \Rightarrow 4mm+19mm=23mm>12mm \\ \Rightarrow 4mm+12mm=16mm<19mm \\ \Rightarrow 19mm+12mm=31mm>4mm \end{gathered}$$

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

Thus, the sides $4mm,19mm,12mm$ will not form a triangle.