An equilateral triangle contains three congruent rectangles. Two distances on its base are given. What fraction is white?
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Solution
The white triangle has a surface of 1/4 of the total.
First recognize that all the small light red triangles are congruent 30-60-90 triangles. Since their short side is 1, their hypotenuse must be 2. Now we can infer the large triangle to have a base of 12 and the inner triangle to have a base of 6.
From the three-fold rotational symmetry it follows that the inner triangle is also equilateral. Hence it is similar to the large triangle and their areas have the proportion (6/12)2=1/4.