18.12 As shown in the figure, in quadrilateral $D F S R$, $\angle R F S=\angle F D R$, $F D=4$, $D R=6$, $F R=5$, $F S=7 \frac{1}{2}$. Then $R S$ is
(A) undetermined.
(B) 4.
(C) $5 \frac{1}{2}$.
(D) 6.
(E) $6 \frac{1}{4}$.
[Solution] Given $\angle R F S=\angle F D R$, and $\frac{4}{6}=\frac{5}{7.5}$ or $\frac{D F}{D R}=\frac{F R}{F S}$, we have $\triangle R F D \backsim \triangle S R F$.
Therefore, $\frac{R S}{R F}=\frac{S F}{R D}$,
so $R S=\frac{S F \cdot R F}{R D}=\frac{5 \cdot 7.5}{6}=6 \frac{1}{4}$.
Thus, the answer is $(E)$.