17・110 Given that the sides of a right triangle are $a, a+d$, and $a+2d$, where $a$ and $d$ are positive numbers, then the ratio of $a$ to $d$ is 
(A) $1: 3$.
(B) $1: 4$.
(C) $2: 1$.
(D) $3: 1$.
(E) $3: 4$.
(10th American High School Mathematics Examination, 1959)
［Solution］From the given and the Pythagorean theorem, we have
$$
(a+2 d)^{2}=(a+d)^{2}+a^{2},
$$

which simplifies to $a^{2}-2 a d-3 d^{2}=0$, or $(a-3 d)(a+d)=0$. From $a-3 d=0$, we get $a: d=3: 1$. Therefore, the answer is (D).