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

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## Solution

A fraction of 3/5 is green.

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

## Poem

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