2022 SSMO Speed Round Problems/Problem 5

Problem

Let $ABCD$ be a square such that $E$ is on $AD$ and $F$ is on $CD.$ If $AE=DF$ and $\frac{[BEF]}{[ABCD]}=\frac{7}{18},$ then the value of $\frac{EF^2}{BC^2}$ can be expressed as $\frac mn$ , where $m$ and $n$ are relatively prime positive integers. Find $m+n$ .

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2022 SSMO Speed Round Problems/Problem 5

Problem

Solution