$17 \cdot 79$ In a right triangle $ABC$, the side $AC$ is divided into eight equal parts, and seven parallel line segments to $BC$ are drawn from each of these points. If $BC=10$, then the sum of the lengths of these seven line segments is
(A) impossible to determine from these data.
(B) 33.
(C) 34.
(D) 35.
(E) 45.
(8th American High School Mathematics Examination, 1957)
[Solution] Let $h_{k}$ be the length of the $k$-th parallel line segment starting from $A$. From $\frac{h_{k}}{\frac{k}{8} \cdot A C}=\frac{B C}{A C}$, we get $h_{k}=\frac{5}{4} k$. Therefore, $\quad \sum_{k=1}^{7} h_{k}=\frac{5}{4} \sum_{k=1}^{7} k=\frac{5}{4} \cdot \frac{8 \cdot 7}{2}=35$. Hence, the answer is $(D)$.