Problem 21

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Problem 21: (2007 AMC 10B, 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?
$\textbf{(A) } \frac{3}{2} \qquad$ $\textbf{(B) } \frac{60}{37} \qquad$ $\textbf{(C) } \frac{12}{7} \qquad$ $\textbf{(D) } \frac{23}{13} \qquad$ $\text{(E) 2}$

Solution

Exercise 21: Solution

Right $\triangle ABC$ has $AB=5, BC=12,$ and $AC=13.$ 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?

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