Pythagoras Theorem

Finding the remaining side of a right-angled triangle

Look at the diagrams below. The areas of the squares are marked inside them (the diagrams are drawn to different scales). How are the squares' areas related to each other?

Did you spot it?

If you add the areas of the smallest two squares you get the area of the largest square.

In any right-angled triangle, the square of the longest side is the sum of the squares of the other two sides. This can be written in the formula:

Where is the longest side.

That is Pythagoras' theorem.

Using Pythagoras theorem to solve problems

You can work out other mathematical problems using Pythagoras' theorem. For instance, if you know two sides of a right-angled triangle, you can find the third like this:

1. square (multiply by itself) the lengths you know
2. add or subtract them
3. find the square root

For these questions you will need to use the button on your calculator.