Question

The sides of a triangle have lengths (in cm) $10,6.5$ and $a$, where $a$ is a whole number. What is the minimum value that $a$ can take?

Answer 1

The lengths of the given two sides are $10\text{cm}$ and $6.5\text{cm}$
We know that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
So, $6.5+a>10$
$a>10-6.5$
$a>3.5$
As $a$ is a whole number, the minimum value it can take is $4$.