A right angled triangle has two short sides of lengths 5cm and 12cm respectively. What is the length of the third side?

13cm. Using Pythagoras theorem a^2 +b^2 =c^2 we substitute our two known lengths into the equation to get 5^2 + 12^2=c^2.
So now we have c^2= 25+144. So c^2 =169. So c=√169 = 13. Don't forget the units!!! So answer is 13cm