AHSME 1996 Problem 15

Two opposite sides of a rectangle are each divided into $n$ congruent segments, and the endpoints of one segment are joined to the center to form triangle $A$. The other sides are each divided into $m$ congruent segments, and the endpoints of one of these segments are joined to the center to form triangle $B$. [See figure for $n=5, m=7$.] What is the ratio of the area of triangle $A$ to the area of triangle $B$?

$\text{(A)}\ 1 \text{(B)}\ m/n \text{(C)}\ n/m \text{(D)}\ 2m/n \text{(E)}\ 2n/m$