Pythagoras Theorem
Quick revise

In any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
i.e.: c² = a² + b² in the following diagram:

A right angled triangle


Find AC in the diagram below.

AB² + AC² = BC²
AC² = BC² - AB²
       = 13² - 5²
       = 169 - 25 = 144
AC  = 12cm

Pythagoras Theorem

This video explains how to work out phytagoras theorem

3D Problems (Higher Tiers)

In higher tier papers, you may be asked to solve 3d problems using Pythagoras.


A cuboid has sides of length 10cm, 2 √11 cm and 5cm. Find the length of a diagonal.

A cuboid

So we want to find AD.

We can draw a right-angled triangle inside the cuboid which has AD as it's hypotenuse. Then we can use Pythagoras.

A  right-angled triangle with AD as it's hypotenuse

To use Pythagoras, we need to know AC and CD. We know that CD is 5 cm. We need to find AC.

We can use Pythagoras to find AC, because if we look at the cuboid from above, we see that AC is the diagonal of a rectangle

AC is the  diagonal of a rectangle

ABC is a right angled triangle, so by Pythagoras, AC2 = AB2 + BC2
= 102 + (2 √11)2 = 100 + 44 = 144

Now we can find AD: AD2 = AC2 + CD2 = 144 + 25 = 169
Therefore AD = 13


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