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The sailing boat

Three congruent right triangles. What fraction is shaded?

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Solution

The shaded fraction is 1/3.

From congruence we know that ∠EAB equals ∠DBC. Therefore line segments EA and BC are parallel. Now we can shear vertex C of triangle AEC along CB to B. The shaded fraction then coincides with triangle AEB, which is one third of the total.

Poem

The sailing boat
Is setting of
To raise and sail in the wind
Chasing the waves
And floating alone
Under the sweet sky smiles
Winds so nice blow and blow
The boat curls on the water
Between the foam and salted pearls
The boat is going it’s own way
Towards the mysteries anyway

Bella

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