Question 80
A trapezium has bases of lengths $1$ and $4$, respectively. It is divided into two trapezia by a cut parallel to the bases, of length $3$. We now wish to divide the two new trapezia, again by cuts parallel to the bases, into $m$ and $n$ trapezia respectively, so that all $m+n$ resulting trapezia have the same area. Determine the least possible value of $m+n$ and the lengths of the cuts needed to achieve it.