4. [6] Right triangle $X Y Z$, with hypotenuse $Y Z$, has an incircle of radius $\frac{3}{8}$ and one leg of length 3 . Find the area of the triangle.
length $x-\frac{3}{8}$ and $3-\frac{3}{8}$. So the hypotenuse has length $x+\frac{9}{4}$, the semiperimeter of the triangle is $x+\frac{21}{8}$, and the area of the triangle is $\frac{3}{8}\left(x+\frac{21}{8}\right)$. But the area can also be calculated as $\frac{3 x}{2}$. Setting these expressions equal, we find $x=\frac{7}{8}$ and the area is $\frac{21}{16}$.