The ragged mountain

A square containing three line segments of given length. What fraction is green?

Scroll down for a solution to this problem.


A fraction of 3/5 is green.

Solution by Quantum ( ? = ! ).

First draw the diagonal. From the Pythagorean theorem it’s length can be deduced as √10. That makes the square side √5 and the total area 5. The two triangles along the diagonal are similar because they have the same angles. They have side proportion 1 : 2. The large one has area 2/3 and the small one 1/6. Now the green area is 5/2+2/3-1/6=3.

Visual solution

Proof without words by David Andriana.


The ragged mountains
Are hanging in the clouds
Rose coloured is the moving land
The sharp peaks
Are shelter to pine forests
Some people head towards the mountains
And work as a porter
In the footpaths and precipitous drops
Sunburnt mountains land
A wide land always be


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