$17 \cdot 94$ In an equilateral triangle, a point is chosen at random, and perpendiculars are drawn from this point to the three sides. The sum of the lengths of these perpendicular segments is
(A) minimum when this point is the centroid of the equilateral triangle.
(B) greater than the height of this triangle.
(C) equal to the height of this triangle.
(D) half the sum of the three sides of this triangle.
(E) maximum when this point is the centroid of this triangle.
(1st American High School Mathematics Examination, 1950)
[Solution] As shown, $P$ is a point inside the equilateral $\triangle ABC$, and the feet of the perpendiculars from $P$ to the three sides are $L, M, N$ respectively. Connect $PA, PB, PC$. If $a$ is the side length of the equilateral triangle and $h$ is the height of one of its sides, then
$$
S_{\triangle ABC}=S_{\triangle PAB}+S_{\triangle PBC}+S_{\triangle PCA} \text{, }
$$

it follows that $h=PL+PM+PN$.
Therefore, the correct choice is $(C)$.