# Throwback maths 1

This is the first of our classical GCSE maths questions; just a straightforward application of Pythagoras.

Solution

The triangle shown is a right-angled triangle and so we can use Pythagoras, which says "the square of the hypotenuse is equal to the sum of the squares of the other two sides", or more succinctly,

$$a^2 + b^2 = c^2$$

In this case, the shorter two sides are known, so we'll say $a = 5$ and $b = 12$. So we get

$$5^2 + 12^ 2 = c^2$$

In turn this gives $c^2 = 169$ and so $c = \sqrt{169} = 13$.

A quicker approach is to spot that 5 and 12 are pairs of numbers making up a Pythagorean triple and so the third number must be 13