A square and a rectangle share two vertices. If the square has twice the area of the rectangle, what’s the angle α?

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## Solution

The angle α is 30°.

The square and the rectangle have equal diagonals, say of length 2. The square then has area 2, whereas the rectangle has area 2sin(90-2α)=2cos(2α). Given it is half of 2, we get cos(2α)=1/2 and so α=30°.

## Poem

Five minuts to midday

The hour has struck

And fades away

The meal is announced

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A break for everyone

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This five minuts

Are a gift and a power