MathDB

A trapezium is given with parallel bases having lengths

1

and

4

. Split it into two trapeziums by a cut, parallel to the bases, of length

3

. We now want to divide the two new trapeziums, always by means of cuts parallel to the bases, in

m

and

n

trapeziums, respectively, so that all the

m + n

trapezoids obtained have the same area. Determine the minimum possible value for

m + n

and the lengths of the cuts to be made to achieve this minimum value.

Problem Statement