18.49 A person, instead of walking around two adjacent sides of a rectangular farm, takes a shortcut along the farm's diagonal, thus saving $\frac{1}{2}$ the length of the longer side of the rectangle. What is the ratio of the shorter side to the longer side?
(A) $\frac{1}{2}$.
(B) $\frac{2}{3}$.
(C) $\frac{1}{4}$.
(D) $\frac{3}{4}$.
(E) $\frac{2}{5}$.
(4th American High School Mathematics Examination, 1953)
[Solution] Let the length and width of the rectangle be $x, y$, then the length of its diagonal is $\sqrt{x^{2}+y^{2}}$. According to the problem, we have $\sqrt{x^{2}+y^{2}}+\frac{x}{2}=x+y$,

After simplification, we get $\quad \frac{3}{4} x^{2}=x y$, i.e., $\frac{y}{x}=\frac{3}{4}$.
Therefore, the answer is $(D)$.