Two overlapping rectangles. What is the proportion of their areas? All triangles in the diagram are right.

Scroll down for a solution to this problem.

## Solution

The rectangles have equal area, so their proportion is 1.

Say the green rectangle has dimensions a and b. Draw a help line from its top left corner parallel to the long orange side. From comparing angles it is easily seen that the orange rectangle has dimensions a/cosα and bcosα. In taking its area, the cosines cancels.