Categories

# The distant Alp

A rectangle containing five triangles. What fraction is brown?

Scroll down for a solution to this problem.

## 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

# Don’t miss these puzzles!

Subscribe to the weekly geometry puzzle e-mail.