18.51 $P$ is a point inside rectangle $A B C D$, with $P A=3$, $P D=4, P C=5$. Then $P B$ equals
(A) $2 \sqrt{3}$.
(B) $3 \sqrt{2}$.
(C) $3 \sqrt{3}$.
(D) $4 \sqrt{2}$.
(E) 2.
[Solution] Draw $EF // AB$ through $P$, and let $DE=c, AE=d, PB=x$. By the Pythagorean theorem, we have $\left\{\begin{array}{l}16-c^{2}=9-d^{2}, \\ 25-c^{2}=x^{2}-d^{2},\end{array}\right.$ which gives $x^{2}-18=0$, so $x=3 \sqrt{2}$ (the negative value has been discarded). Therefore, the answer is $(B)$.