A triangle with an inscribed square. What fraction is yellow?

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## Solution

The yellow fraction is 10/27.

This solution draws the altitude HA. Because of tan(α)=1/2 and the known hypotenuse of 3 of right triangle HGA, we can calculate HA and HG.

Triangle EAH is isosceles, so we also have EH. Now the whole triangle EAG has known base and height and its area can be calculated as 27/10. The required fraction is simply the reciprocal of that.

## Poem

The crane is flying very high

Over the houses, the bridges, to the sky

He is made of iron and steel

And caries stand, stones and wheels

Workers are proud to drive the crane

It’s an honour, a favour like a plane

He’s as beautiful as a praying mantis

So elegant, a metamorphosis.