Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 52. (October 2005)

K. 52. The Figure shows the planned footpaths for a park in a city. What is the total length of the paths to be constructed if the lengths of the two kinds of segments marked in the diagram are 60 metres and 30 metres, respectively?

(6 pont)

Deadline expired on November 10, 2005.

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

Megoldás: Legyen a kör sugara 30+x méter. Az x, 60, 30+x oldalú derékszögű háromszögre felírva a Pitagorasz-tételt: x2+602=(x+30)2, ebből x=45 méter. Az összes megépítendő út hossza tehát: 10.75+6.60+150.\pi\approx1581,24 méter.


210 students sent a solution.
6 points:68 students.
5 points:43 students.
4 points:37 students.
3 points:18 students.
2 points:12 students.
1 point:13 students.
0 point:17 students.
Unfair, not evaluated:2 solutions.

Problems in Mathematics of KöMaL, October 2005