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2022 SSMO Speed Round Problems/Problem 5: Difference between revisions

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==Problem==


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

Revision as of 18:14, 2 May 2025

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 $m+n$.

Solution

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