Mathematical and Physical Journal
for High Schools
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Problem K. 257. (September 2010)

K. 257. The surface area of a cuboid is 2010 cm2. If each edge is increased by 1 cm, the surface area will be 2251.52 cm2. Find the sum of the lengths of three different edges of the original cuboid.

(6 pont)

Deadline expired on October 11, 2010.

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

Megoldás. Az eredeti téglatest éleinek hosszát (centiméterekben kifejezve) jelölje \(\displaystyle a\), \(\displaystyle b\) és \(\displaystyle c\). A téglatestet megnövesztve a felszíne \(\displaystyle F^*=2\big( (a+1)(b+1)+(b+1)(c+1)+(c+1)(a+1)\big)=2(ab +a+b+1+bc+b+c+1+ca+c+a+1)=2(ab+bc+ca+2(a+b+c)+3)\). Az eredeti téglatest \(\displaystyle F=2(ab+bc+ca)\) felszínét felhasználva kapjuk, hogy \(\displaystyle F^*=F+4(a+b+c)+6\). A feladatan megadott adatokat felhasználva \(\displaystyle a+b+c=\mathbf{58.88}\) cm volt az eredeti téglatest éleinek összhossza.


281 students sent a solution.
6 points:160 students.
5 points:68 students.
4 points:22 students.
3 points:6 students.
2 points:5 students.
1 point:2 students.
0 point:2 students.
Unfair, not evaluated:16 solutions.

Problems in Mathematics of KöMaL, September 2010