Triangle ABC has perimeter 20 cm. AB = 7 cm. BC = 4 cm. By calculation, deduce whether triangle ABC is a right-angled triangle.

This is a question I recently tackled with one of my tutees from the edexcel GCSE specimen papers. I would begin to tackle any geometry question like this by drawing the triangle in question. We are given three key pieces of information, which should be written down so we can refer back to it. We know the triangle's perimeter, and the length of two of its sides. The natural progression here is to calculate the length of the third side. We see 20-(7+4)=9, so we can note the side AC has length 9cm. This means it would be the hypotenuse of a right angled triangle, so we can annotate our triangle. Now we consider the properties of a right angled triangle, and Pythagoras in particular. For any right angle triangle a^2+b^2=c^2, where c is the hypotenuse. So we substitute in our values, and find 4^2+7^2=65, not the desired 81. As such we can say the triangle can't be right angled by Pythagoras.