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

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## Solution

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.

## Poem

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