Find the length of the hypotenuse of a right angled triangle which has other two sides of length 5 and 12.

When we have 2 sides of a right angled triangle, we can use Pythagoras' Theorem to find the third missing side. This theorem states that if we label the hypotenuse (the side opposite the right angle) as c, and the other two sides as a and b, then a² + b² = c². So, looking at the values given in the question we have a = 5 and b = 12. Lets substitute this into Pythagorus' Theorem. this gives c² = 5² + 12² = 25 + 144 = 169. So, c we can find c by square rooting 169. This gives c = 13 or c = -13, but as a length must be positive, we must have c = 13! So the length of the hypotenuse is 13.