A Box of Rati-O's

Geometry Level 3

Rectangle $$\mathbb{A}$$ is inscribed in rectangle $$\mathbb{B}$$, so that each of the vertices of $$\mathbb{A}$$ lies on a different side of $$\mathbb{B}$$.

The length-to-width ratio for $$\mathbb{A}$$ is 2:1, and the length-to-width ratio for $$\mathbb{B}$$ is 3:2.

Find the ratio of the area of $$\mathbb{A}$$ to the area of $$\mathbb{B}$$.

If your answer is $$a: b$$, where $$a$$ and $$b$$ are positive coprime integers, enter $$a+b$$ as your answer.

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