The hanging door

Two congruent rectangles support a third rectangle. What fraction is blue?

Scroll down for a solution to this problem.


The blue fraction is 8/13.

The first step is to recognise that the two shown angles are equal. This gives rise to two similar triangles in the standing block. Setting the short side to 1, we infer x/1=1/y.

Next we enlarge the upper triangle to include part of the lying block and find x/1=(x+y)/(1+y). The two equations can be worked out to find x=y=1.

So the small blocks have area 2 and the large block has area 4. Their overlap is 3/2, so we find for the blue fraction 4/(4+2+2-3/2)=8/13.


The hanging door
What’s happening behind the door?
Are we going,
Are we coming?
Doors are closed at night
Hanging or backdoor
Past is gone
Future is open
Don’t disturb !
Yes disturb me !
I open my door
For love
For peace
For friendship


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