Ray of light

A triangle with an inscribed triangle with a parallel side. What fraction is yellow?

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The yellow fraction is 6/25.

Solution by Bannu.

First, use the parallel lines to establish that the line segments at the bottom also have proportion 3 : 2. Now naming the area on the right 4A, having the same height, the yellow triangle must have area 3/2*4A=6A.

Using the side proportion, the upper triangle is seen to be 3/2*(6A+4A)=15A. The required fraction 6A/(6A+4A+15A)=6/25.


A ray of light
Escaped from the sun slowly
To warm the earth gently
Like a brilliant star daily
And bringing light hopefully
As well as feelings of life, love, easily
The ray of light has in it’s hand
Our destiny
To share it with all you if possibly
Without words, silently !


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