Challenge Level

*Nicely Similar printable sheet*

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?

*For another way to see this arrangement of right-angled triangles you may like to look at the problem called a Matter of Scale .*