MathDB

4 of the rods with lengths 1, 2, 3, 4, 5, 6, 7, 8 for a trapezoid

Source: 2020 Dürer r Math Competition Finals Day2 E16 https://artofproblemsolving.com/community/c1622639_2020_

January 7, 2022

trapezoidtriangle inequalitygeometry

Problem Statement

Dora has

8

rods with lengths

1, 2, 3, 4, 5, 6, 7

and

8

cm. Dora chooses

4

of the rods and uses them to assemble a trapezoid (the

4

chosen rods must be the

4

sides). How many different trapezoids can she obtain in this way?
Two trapezoids are considered different if they are not congruent.