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2025 SSMO Team Round Problems/Problem 6

Revision as of 11:32, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== The rhombus <math>PQRS</math> has side length <math>3</math>. The point <math>X</math> lies on segment <math>PR</math> such that line <math>QX</math> is perpendic...")
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Problem

The rhombus $PQRS$ has side length $3$. The point $X$ lies on segment $PR$ such that line $QX$ is perpendicular to line $PS$. Given $QX=2$, the area of $PQRS$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

Solution

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