$ABCD$ is a trapezium where $AB$ $||$ $CD$. Suppose $[\Delta BOC] = \frac{25}{9}$, and let $AB = b$, $CD = a$ where $a < b$.

Question

$ABCD$ is a trapezium where $AB$ $||$ $CD$. Suppose $[\Delta BOC] = \frac{25}{9}$, and let $AB = b$, $CD = a$ where $a < b$. Find the value of $\frac{b}{a}$.

What I Tried: Here is a picture :-

I really have no idea on how to start this. I might proceed by giving variables to the side lengths and use similarity and area, but I am sure this will be length and quite complicated. There is as little information as possible, and I got no idea how to solve it.

Can anyone help me? Thank You.

Answer 1

This is not an answer

As observed in the comments the trapezoid is not unique. See the picture below

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