Question

The sides of a triangle have lengths (in cm) as 10, 6.5, and a, where a is a prime number. Find the maximum value of 'a', which it can take.
[2 Marks]

Answer 1

We know, the sum of any two sides in a triangle is always greater than the third side.
$\left[0.5\right]$

So, 10 + 6.5 > a
$\Rightarrow 16.5>a$
[1 Mark]
$\left[0.5\right]$

'a' is a prime number and it's less than 16.5. So, its maximum value will be 13.
[1 Mark]