Mathematical and Physical Journal
for High Schools
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# Problem P. 4846. (May 2016)

P. 4846. An equilateral triangle is cut from a uniform sheet. The triangle is hung at one point $\displaystyle P$ at its rim. The distance between point $\displaystyle P$ and one of the vertices of the triangle is $\displaystyle x$ times the side of the triangle.

The vertical line through point $\displaystyle P$ cuts the triangle into two parts. What is the ratio of the masses of these two parts? When will this ratio have an extremum and what is this extremum?

(5 pont)

Deadline expired on June 10, 2016.

### Statistics:

 29 students sent a solution. 5 points: Balogh Menyhért, Bekes Nándor, Bukor Benedek, Di Giovanni András, Édes Lili, Elek Péter, Fehér 169 Szilveszter, Ghada Alshalan, Jakus Balázs István, Kasza Bence, Kluèka Vivien, Marozsák Tóbiás , Molnár Mátyás, Németh 777 Róbert, Németh Flóra Boróka, Olosz Adél, Páhoki Tamás, Póta Balázs, Pszota Máté, Sal Kristóf, Tomcsányi Gergely, Varga-Umbrich Eszter, Wiandt Péter, Zöllner András. 3 points: 2 students. 2 points: 1 student. Unfair, not evaluated: 2 solutions.

Problems in Physics of KöMaL, May 2016