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
