Mathematical and Physical Journal
for High Schools
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# Problem C. 924. (December 2007)

C. 924. The areas of the rectangles obtained by intersecting a certain cuboid with a plane passing through two parallel edges may be t1=60, , or . Calculate the volume and surface area of the cuboid.

(5 pont)

Deadline expired on January 15, 2008.

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

Megoldás. Tudjuk, hogy , , . Vagyis a következő egyenletrendszert írhatjuk fel:

a2b2+a2c2=3600,

b2c2+a2b2=2448,

a2c2+b2c2=1440.

A három egyenlet összegének a fele: a2b2+a2c2+b2c2=3744. Ebből az egyenletből az egyenletrendszer egy-egy egyenletét kivonva kapjuk, hogy b2c2=144, a2c2=1296, a2b2=2304. Azaz: bc=12, ac=36, ab=48.

A=2(ab+ac+bc)=2(48+36+12)=192.

### Statistics:

 262 students sent a solution. 5 points: 202 students. 4 points: 22 students. 3 points: 8 students. 2 points: 11 students. 1 point: 9 students. 0 point: 7 students. Unfair, not evaluated: 3 solutions.

Problems in Mathematics of KöMaL, December 2007