Problem K. 452. (February 2015)
K. 452. A silo for storing winter food for cattle is attached to one corner of a rectangular stable. The silo is shaped like a regular triangular prism, with base edges of length 3 metres. The longer side of the stable is 9 metres. With a 9-metre-long rope, a goat is tied to the point where the silo joins with the stable (see the figure). The goat cannot break the rope, and the rope will not stretch. The buildings are surrounded with grass, and there is no fence or any other obstacle hindering the goat from grazing. Find the area that the goat can graze.
Deadline expired on March 10, 2015.
77 students sent a solution. 6 points: Agócs Katinka, Ágoston Tamás, Bärnkopf Teréz, Beleznay Levente, Braun Dániel, Csuha Boglárka, Encz Koppány, Farkas Lilla, Fekete Balázs Attila, Hegedűs 330 Marcell, János Zsuzsa Anna, Kozma Dávid Márk, Maksa Gergő, Mészáros Melinda, Németh Csilla Márta, Perényi Gellért, Péri Gergő Gábor, Pongrácz Edina, Posch Levente Ágoston, Slenker Balázs, Szarka Álmos, Szűcs 865 Eszter, Tamási Kristóf Áron, Valentiny Anett, Wenczel Kata. 5 points: 33 students. 4 points: 13 students. 3 points: 4 students. 2 points: 2 students.