Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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Problem C. 847. (March 2006)

C. 847. Find a line that halves both the area and the perimeter of the ``Egyptian'' triangle (the sides of which are 3, 4, 5).

(5 pont)

Deadline expired on April 18, 2006.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás: Ha a kerületet felezni akarjuk, akkor (a rövidebbik befogón keletkezett két szakasz hosszát x-szel és (3-x)-szel jelölve) az átfogón keletkező két szakasz hossza 3+x és 2-x.

A két derékszögű háromszög hasonlóságából $m={4\over5}\cdot(3+x)$ . A terület felezése miatt pedig $(3-x)\cdot{4\over5}(3+x)\cdot{1\over2}=3$ , ahonnét $x=\sqrt{1,5}$ .

Statistics:

210 students sent a solution.

5 points: 127 students.

4 points: 14 students.

3 points: 12 students.

2 points: 6 students.

1 point: 6 students.

0 point: 45 students.

Problems in Mathematics of KöMaL, March 2006

210 students sent a solution.
5 points:	127 students.
4 points:	14 students.
3 points:	12 students.
2 points:	6 students.
1 point:	6 students.
0 point:	45 students.