Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 422. (September 2014)

K. 422. Two squares of sides $\displaystyle a$ and $\displaystyle b$ are placed next to each other and then cut into five plane figures altogether with two line segments of length $\displaystyle c$, as shown in the figure. Show that it is possible to build, without gaps or overlaps, a square of side $\displaystyle c$ out of the five pieces.

(6 pont)

Deadline expired on October 10, 2014.

### Statistics:

 130 students sent a solution. 6 points: Fekete Balázs Attila, Kós Anna, Kubovics Márton, Perényi Gellért, Sántha 001 Balázs, Sisák László Sándor, Szarka Álmos, Szilágyi Botond, Valkó Bence. 5 points: Bácskai Zsombor, Cu Le Dieu Huong, Encz Koppány, Harsányi Benedek, János Zsuzsa Anna, Sepp Márton. 4 points: 18 students. 3 points: 17 students. 2 points: 16 students. 1 point: 46 students. 0 point: 14 students. Unfair, not evaluated: 4 solutions.

Problems in Mathematics of KöMaL, September 2014