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
You don’t have to steal the fire Take care !
The Pandora box is made of
You can leave it closed !