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2023 WSMO Team Round Problems/Problem 7

Revision as of 15:37, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== In triangle <math>ABC</math> with <math>AB = 13,AC = 14</math>, and <math>BC = 15,</math> a rectangle <math>WXYZ</math> is inscribed such that the area of <math>W...")
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Problem

In triangle $ABC$ with $AB = 13,AC = 14$, and $BC = 15,$ a rectangle $WXYZ$ is inscribed such that the area of $WXYZ$ is maximized. If the minimum possible value of $\frac{WX}{XY}$ is $\frac{m}{n},$ for relatively prime positive integers $m$ and $n,$ find $m+n.$

Solution

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