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.
