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

diagram with similar right-angled triangles


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 .