Pandora’s box

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

Scroll down for a solution to this problem.


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 11a2/2, whereas the total area is 9a2, leading to a fraction of 11/18.


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
And passion
And lies
And jealousy
But remember
You can leave it closed !


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