# Right-Angled Request

Weekly Problem 26 - 2006

How many right angled triangles are formed by the points in this diagram?

How many right angled triangles are formed by the points in this diagram?

## Problem

Image

The figure shows a rectangle PRSU with a line QT, which divides the rectangle into two squares.

How many right-angle triangles can be drawn using any three points P, Q, R, S, T, U as corners?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

## Student Solutions

Four right-angled triangles can be drawn in each of the squares, plus four formed from two adjacent sides of the rectangle - that makes 12.

Then there are two right-angled triangles formed by joining the points UQS and PTR.

This makes a total of 14 triangles.