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Intermediate

Five to twelve

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
School is over
The offices will close
A break for everyone
In the middle of the day
A special moment
To relax
To meat eachother
This five minuts
Are a gift and a power

Bella

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