Two squares share two vertices. A line segment connects two other vertices, forming the base of three triangles. What is the proportion green : white : red?

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## Solution

Green : white : red is 3 : 1 : 2.

First draw the line segment EF parallel and congruent to DC. From congruence of triangles EFH and CHD, we get a=b+c. From similarity of triangles JFI and CDI we get a+b=2c. These two equations give a=3b and c=2b. Because the green, white and red triangles all have equal height, we get the desired area proportion.

## Poem

It can be for Forza Italia

White and snowy

Green for mountains and hills

Red for the blood that flew during the wars

Another flag has 3 colours too

The french flag

Blue for bourgeoisie

Red for nobility

White for clergy

The flag from France and Italy

A symbol for each country