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Show that $S$ and $S^{'}$ are disjunctive.

Source: Moldova TST 1999

August 7, 2023

geometryperimeter

Problem Statement

Let

ABC

be an equilateral triangle and

n{}, n>1

an integer. Let

S{}

be the set of the

n-1

lines parallel with

BC

that cut

ABC

in

n{}

figures with equal areas and

S^{'}

be the set of the

n-1

lines parallel with

BC

that cut

ABC

in

n{}

figures with equal perimeters. Show that

S{}

and

S^{'}

are disjunctive.

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