Mathematical and Physical Journal
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Problem B. 4333. (February 2011)

B. 4333. The lengths of two sides of a triangle are 12 and 18. The lengths of two sides of another, similar but not congruent, triangle are also 12 and 18. Find the lengths of the third sides of the triangles.

(Suggested by Á. Besenyei, Budapest)

(3 pont)

Deadline expired on March 10, 2011.


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

Megoldás. A nagyobbik háromszög leghosszabb oldala hosszabb kell legyen a kisebbik háromszög bármelyik oldalánál, vagyis hosszabb, mint 18. Hasonlóan a kisebbik háromszög legrövidebb oldala rövidebb, mint 12. Tehát a kisebbik háromszög oldalai \(\displaystyle a<12<18\), a nagyobbik háromszög oldalai pedig \(\displaystyle 12<18<b\). A hasonlóság miatt

\(\displaystyle \frac{a}{12}=\frac{12}{18}=\frac{18}{b},\)

ahonnan \(\displaystyle a=8\), \(\displaystyle b=27\) adódik.


Statistics:

196 students sent a solution.
3 points:116 students.
2 points:76 students.
1 point:2 students.
0 point:2 students.

Problems in Mathematics of KöMaL, February 2011