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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 points)

This problem is for grade 9 students only.

Deadline expired on 10 November 2005.

Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás: Legyen a kör sugara 30+x méter. Az x, 60, 30+x oldalú derékszögû háromszögre felírva a Pitagorasz-tételt: x2+602=(x+30)2, ebbõl x=45 méter. Az összes megépítendõ út hossza tehát: 10.75+6.60+150.1581,24 méter.

Statistics on problem K. 52.
 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

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