Two squares of area 1 and 4 are inscribed in their own triangle and placed as shown. What fraction is coloured?

Solution

The coloured fraction is 4/9.

This visual solution uses the following elements:

• The small standing triangle and the larger lying one are similar and have length proportion 1 : 2.
• All triangles are similar and have sides with side proportion 1 : 2.
• The larger lying triangle has area 9 and thus coloured fraction 4/9.
• Because of the similarity this is also the total coloured fraction.