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2007 AMC 10B Question 21

AMC10 · 2007 AMC 10B

Question 21

Right $\triangle ABC$ has $AB=3,$ $BC=4,$ and $AC=5.$ Square $XYZW$ is inscribed in $\triangle ABC$ with $X$ and $Y$ on $\overline{AC},$ $W$ on $\overline{AB},$ and $Z$ on $\overline{BC}.$ What is the side length of the square?

Question illustration
  1. $\dfrac{3}{2}$
  2. $\dfrac{60}{37}$
  3. $\dfrac{12}{7}$
  4. $\dfrac{23}{13}$
  5. $2$