Two squares share a vertex. An isosceles triangle connects three others. What fraction is blue?
Scroll down for a solution to this problem.
The blue fraction is 1-√3/2, which is approximately 0,13.
The first part of the solution is to proof that the isosceles triangle ABC is in fact an equilateral triangle. This involves the following steps:
- Triangles KBC and JCE are congruent because of AAS.
- JC is congruent with LC, because of the larger square.
- Triangles KAC and KBC are congruent because of SAS.
- All sides of triangle ABC are congruent.
Using the above, we can easily fill in the lengths as shown, where for convenience we have taken the small square to be a unit square. The blue area is √3/6, whereas the large non-blue square measures (1/2+√3/2)2=1+√3/2. The required fraction follows.
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