Question

L= 12 cm and M= 5 cm. What is n?

Answer 1

This is a perfect place to use Pythagoras' rule.  When you do that, the answer rolls out immediately, and if you don't catch it , it falls off the edge of the desk.

Pythagoras' Theorem:

In a RIGHT triangle, the square of the longest side is equal to

             (one short side)² + (other short side)² .

This is EXACTLY what you need, because MLN is a RIGHT triangle,
you know the length of both sort sides, and you need to find the
length of the longest side.

M =  5 ,    M²  =    25
L = 12 ,     L²  =  144

Add the squares together:    25 + 144  =  169

Pythagoras says that 169 is the square of N .

When you take its square root, you'll have the length of 'N'.

Answer 2

C² = a² + b²
c² = 5² + 12²
c² = 25 + 144
c² = 169
 c = 13 cm