Question

The lengths of two sides of a triangle are $12cm$ and $15cm$. Between what two measures should the length of the third side fall?

Answer 1

Let the given lengths of triangle be $AB=12cm$ and $BC=15cm$ and the third side be $CA$.
Since, In a triangle, the sum of the lengths of either two sides is always greater than the third side.
So, $CA>12+15$
$\Rightarrow CA>27$ .......(i)
and also, the difference of the lengths of either two sides is always lesser than the third side.
So, $CA<15-12$
$\Rightarrow CA<3$......(ii)
From inequality (i) and (ii), we get
$3<CA<27$
Therefore, those two measures are $3cm$ and $27cm$.