A square containing five other squares. What fraction is coloured?

Scroll down for a solution to this problem.

## Solution

The coloured fraction is 11/18.

The solution is a matter of careful administrating square sides and congruent triangles. Above the diagonal we marked three congruent right abc-triangles. Below it we marked two congruent right aed-triangles.

Equating the left side of the containing square to the top gives 2a+b=a+2b. This gives a=b. Using the Pythagorean theorem in the abc-triangles, we find that c=a√2.

The bottom side must be 3a, giving e=a/2. Using the Pythagorean theorem in the aed-triangles, we find that d=a√5/2.

Now the total coloured area adds up to 11a^{2}/2, whereas the total area is 9a^{2}, leading to a fraction of 11/18.

## Poem

The Pandora box

Keeps all pains and tragedies

When you open it

You can find sufferings of the world

And catastrophes

You don’t have to steal the fire Take care !

The Pandora box is made of

Beauty

And passion

And lies

And jealousy

But remember

You can leave it closed !

## 2 replies on “Pandora’s box”

11/18?

Correct. Well done.