Magyar Information Contest Journal Articles

# Problem B. 4375. (September 2011)

B. 4375. Let a and b be the legs of a right-angled triangle, and let m be the height drawn to the hypotenuse c. Which line segment is longer, a+b or m+c?

Suggested by P. Székely, Budapest

(3 pont)

Deadline expired on October 10, 2011.

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

Megoldás. A háromszög területét $\displaystyle {1 \over2} ab$ és $\displaystyle {1 \over 2}cm$ alakban is felírhatjuk. Így a Pithagorasz-tétel alapján

$\displaystyle (a+b)^2=a^2+b^2+2ab=c^2+2cm<c^2+2cm+m^2=(c+m)^2,$

vagyis $\displaystyle a+b<m+c$.

### Statistics:

 272 students sent a solution. 3 points: 237 students. 2 points: 6 students. 1 point: 10 students. 0 point: 10 students. Unfair, not evaluated: 9 solutions.

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