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Whiskey on the rocks

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-√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:

  1. Triangles KBC and JCE are congruent because of AAS.
  2. JC is congruent with LC, because of the larger square.
  3. Triangles KAC and KBC are congruent because of SAS.
  4. 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.

Visual solution

Visual solution by David Andriana

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

Bella

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