**Start revising A-level & GCSE with 7 million other students**

# Pythagoras' Theorem

## You are here

## Pythagoras' Theorem

Pythagoras was a very brainy Greek gentleman who discovered loads of mathematical stuff, but the discovery most people know him for (and you need to learn!)is called **Pythagoras' Theorem.**

Basically, he discovered that if you stick squares onto the sides of **any** right-angled triangle the **areas ** of the two smaller squares are **equal** to the area of the large one.

Or, to put it in technical terms, '**the square on the hypotenuse is equal to the sum of the squares on the other two sides.'**

Now you just need to be able to use it!

Here's a few examples. The working shows each step needed to find the missing side.
In each example, the missing side is called **x:**

**First put the numbers into the formula:**

**Do the addition:**

**Now square root both sides to find x giving the answer to a sensible number of decimal places:**

8.94 = x

So x = 8.94cm to two decimal places.

Here's another one where you are looking for one of the smaller sides, **not** the Hypotenuse!

**As before, put the numbers into the formula:**

**Now subtract 4.4 ^{2 }from both sides:**

**Do the subtraction:**

**Square root****both sides to find x:**

x = 9.86cm to two decimal places.

Try this one yourself - type the length of the missing side into the space provided.