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

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## Solution

The yellow fraction is 6/25.

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.

## Poem

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 !