Question

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

$12cm,14cm,15cm$.

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:

$$\begin{gathered} \Rightarrow 12cm+14cm=26cm>15cm \\ \Rightarrow 12cm+15cm=27cm>14cm \\ \Rightarrow 14cm+15cm=29cm>12cm \end{gathered}$$

Since, the sum of lengths of any two sides is greater than the third side,

Therefore, triangle having side lengths $12cm,14cm,15cm$ is possible with these lengths as sides of the triangle.