Mathematical and Physical Journal
for High Schools
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Problem K. 307. (November 2011)

K. 307. The rectangle in the figure is dissected into squares. The area of square A is 196 cm2, that of square B is 16 cm2, and the area of square C is 81 cm2. What is the area of the rectangle?

(6 pont)

Deadline expired on December 12, 2011.

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

Megoldás. Az \(\displaystyle A\) négyzet oldala \(\displaystyle 14\ cm\), a \(\displaystyle B\) négyzet oldala \(\displaystyle 4\ cm\), a \(\displaystyle C\) négyzet oldala \(\displaystyle 9\ cm\). A \(\displaystyle D\) négyzet oldala \(\displaystyle A\) és \(\displaystyle B\) oldalának összege, azaz \(\displaystyle 18\ cm\), tehát a téglalap egyik oldala \(\displaystyle 14+18=32\ cm\) hosszúságú. Az \(\displaystyle E\) négyzet oldala \(\displaystyle A\) és \(\displaystyle B\) oldalának különbsége, azaz \(\displaystyle 10\ cm\), tehát a téglalap másik oldalának hossza \(\displaystyle 14+10+9=33\ cm\). A téglalap területe tehát \(\displaystyle 1056\ cm^2\).


298 students sent a solution.
6 points:210 students.
5 points:27 students.
4 points:30 students.
3 points:21 students.
2 points:6 students.
1 point:1 student.
0 point:2 students.
Unfair, not evaluated:1 solutions.

Problems in Mathematics of KöMaL, November 2011