Cut-Up Square

Weekly Problem 15 - 2015
In the diagram, two lines have been drawn in a square. What is the ratio of the areas marked?
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Problem

Image
Cut-Up Square


The diagram shows a square, a diagonal and a line joining a vertex to the midpoint of a side. What is the ratio of area P to area Q?

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