1. In triangle $D E F$, the heights (emanating, respectively, from vertices $D, E$, and $F$) measure, in order, 84, 80, and 81 meters. Indicating with $d, e, f$ the lengths, respectively, of sides $E F, F D, D E$, which of these inequalities is correct?
(A) $e<f<d$
(D) $f<e<d$
(B) $d<f<e$
(E) $e<d<f$
(C) $d<e<f$
(1) The correct answer is $(B)$.

Since in a triangle the product of each side with its corresponding height is the same (i.e., twice the area), it follows that the height relative to the shortest side must be the longest, and vice versa. The correct order is therefore $d<f<e$.

Question proposed by Paolo Francini.