若复数 $z=\frac{(1+\mathrm{i})^{2}}{3+4 \mathrm{i}}$, 则 $|z|=(\quad)$

$\begin{array}{llll}\text {
由题得 $z=rac{(1+i)^{2}}{3+4 i}=rac{2 i}{3+4 i}=rac{2 i(3-4 i)}{(3+4 i)(3-4 i)}=rac{8+6 i}{25}$,所以 $|z|=\sqrt{\left(rac{8}{25}
ight)^{2}+\left(rac{6}{25}
ight)^{2}}=rac{10}{25}=rac{2}{5}$, 故选 C.