Pythagoras' theorem

Three, four, five. Make a triangle with these sides, and the corner between the three and the four is always a perfect right angle. Why?

In a right angled triangle, the longest side is opposite the right angle. It's called the hypotenuse, C. The shorter sides are A and B.

Now build a square on each side. The square on the three holds nine tiles. The square on the four holds sixteen. Now watch. Nine plus sixteen makes twenty five, and every single tile fits the square on the hypotenuse.

That's Pythagoras' theorem. A squared plus B squared equals C squared. The two smaller squares always add up to the biggest one.

Let's find a hypotenuse. The short sides are six and eight. Six squared is thirty six. Eight squared is sixty four. Add them to get one hundred, and the square root of one hundred is ten.

To find a shorter side, subtract instead. The hypotenuse is thirteen and one side is five. One hundred and sixty nine, take away twenty five, leaves one hundred and forty four. Its square root is twelve.

Builders use this all the time. A ladder against a wall is the hypotenuse of a right angled triangle. A two point five metre ladder, with its foot point seven metres out, reaches two point four metres up.

But be careful. It only works when there's a right angle. Close the corner, and the third side gets shorter than five. Open it wider, and it gets longer.

So remember. The hypotenuse is the longest side, opposite the right angle. A squared plus B squared equals C squared. Add the squares to find the hypotenuse, and subtract to find a shorter side.