Two squares share a vertex. An isosceles triangle connects three others. What fraction is blue?

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## Solution

The blue fraction is 1-β3/2, 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 β3/6, whereas the large non-blue square measures (1/2+β3/2)^{2}=1+β3/2. The required fraction follows.

## Visual solution

## Poem

Just a whisky on the rocks

Whisky is not only a simple word

It’s gaelic roots means water

Whisky remembers distillation

And moments with elation

Some scottish alcoholization

Meeting in a glass liquid amber, and icy rocks for salvation

It’s the nicest drink for celebrations