benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / A line in the plane of a triangle T is called an …T into two regions having equal area and equal perimeter. Find positive integers a>b>c, with a as small as possible, such that the…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

A line in the plane of a triangle TT is called an \emph{equalizer} if it divides TT into two regions having equal area and equal perimeter. Find positive integers a>b>ca>b>c, with aa as small as possible, such that there exists a triangle with side lengths a,b,ca, b, c that has exactly two distinct equalizers.
Plain-text mathematical notation (without MathML)
A line in the plane of a triangle T is called an \emph{equalizer} if it divides T into two regions having equal area and equal perimeter. Find positive integers a>b>c, with a as small as possible, such that there exists a triangle with side lengths a,b,c that has exactly two distinct equalizers.
Original LaTeX notation
A line in the plane of a triangle $T$ is called an \emph{equalizer} if it divides $T$ into two regions having equal area and equal perimeter. Find positive integers $a>b>c$, with $a$ as small as possible, such that there exists a triangle with side lengths $a, b, c$ that has exactly two distinct equalizers.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
7251b6d5-4f48-521b-88d8-279cf4ef42ab
task_key
test--7251b6d5-4f48-521b-88d8-279cf4ef42ab
task_revision_id
1
config / split
/ test

Official source

initial import