18.35 Given that one diagonal of a rhombus is twice the length of the other, if $k$ represents the area of this rhombus, then its side length is
(A) $\sqrt{k}$.
(B) $\frac{\sqrt{2 k}}{2}$.
(C) $\frac{\sqrt{3 k}}{3}$.
(D) $\frac{\sqrt{4 k}}{4}$.
(E) None of the above.
(12th American High School Mathematics Examination, 1961)
[Solution] Let the side length of the rhombus be $a$, and the two diagonals be $d$ and $2d$. According to the problem,
$\frac{1}{2} \cdot d \cdot 2d = k$, which means $d^2 = k$.
Also, $a^2 = d^2 + \left(\frac{d}{2}\right)^2 = k + \frac{k}{4} = \frac{5}{4}k$,

thus $a = \frac{\sqrt{5k}}{2}$.
Therefore, the answer is $(E)$.