A rectangle containing five triangles. What fraction is brown?

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## Solution

The brown fraction is 3/20.

First we recognize an equilateral triangle surrounded by four 30-60-90 triangles. Of the latter it is well known that the sides have proportion 1 : √3 : 2. If one sets the equilateral side to 1, the other lengths can be deduced from this proportion as shown.

The brown triangle then has area √3/8. The rectangle is 5√3/6. The required fraction follows.

## Visual solution

We were pleased to receive a completely visual solution from Uila, showing that the rectangle can be divided into 80 congruent triangles respecting all the triangle boundaries. Twelve of them are brown.

## Poem

Our geometrical poet Belladonna composed the following lyrical poem:

Le fier glacier domine l’horizon

Les Alpes en dentelles, notre passion

Y fleurissent l’edelweiss et la valériane

Ainsi que la gentiane.

Silence ouaté, éternel

Sommets immaculés tournés vers le ciel

Métaphore étoilée brune et verte,

Ici représentée

Bella