# [CMC ARML 2020 I2] Equal Areas

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Let $ABCD$ be a quadrilateral with side lengths $AB=2$, $BC=5$, $CD=3$, and suppose $\angle B=\angle C=90^\circ$. Let $M$ be the midpoint of $\overline{AD}$ and let $P$ be a point on $\overline{BC}$ so that quadrilaterals $ABPM$ and $DCPM$ have equal areas. Compute $PM$.