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Intermediate

Mini and Maxi

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

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Solution

The coloured fraction is 4/9.

Visual solution by David Andriana.

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.
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