In the diagram below, a right-angled triangle has a line descending from its right angle, perpendicular to the hypotenuse.

If the hypotenuse length is 100cm, and if the line splits the base into 36cm and 64cm parts, what are the side lengths of the original right-angled triangle?

Mathematical reasoning & proof. Circle properties and circle theorems. Polynomial functions and their roots. Similarity and congruence. Creating and manipulating expressions and formulae. Regular polygons and circles. Pythagoras' theorem. Inequalities. Simultaneous equations. Sine rule & cosine rule.