Let's construct a rhombus, given its side $a$ and knowing that the side is the geometric mean of the diagonals.
Let the height of the rhombus be $m$, and the diagonals be $e$ and $f$. According to the problem, $e f=a^{2}$, and from the area formula, $e f=2 a m$, thus

$$
2 a m=a^{2}
$$

from which

$$
m=\frac{a}{2}
$$

With the side $a$ and the height $m=\frac{a}{2}$, the rhombus can be easily constructed. (Since $\sin \alpha=\frac{a}{2} / a=\frac{1}{2}$, the angles of the rhombus are: $30^{\circ}$, or $\left.150^{\circ}.\right)$

Iren Fekete (Bp. XIX., Dolgozó Városi ip. techn. I. o. t.)