Notam latura patratului cu x.
Scriem aria triunghiului ABC in doua moduri:
[tex]A_{ABC}=\dfrac{BC\cdot AD}{2}=36\ cm^2[/tex]
[tex]A_{ABC}=A_{MNPQ}+A_{PNC}+A_{PAQ}+A_{MQB}\Rightarrow[/tex]
[tex]\Rightarrow 36=x^2+\dfrac{x\cdot NC}{2}+\dfrac{x\cdot BM}{2}+\dfrac{x(6-x)}{2}[/tex]
[tex]72=2x^2+x(NC+BM)+x(6-x)[/tex]
[tex]72=2x^2+x(12-x)+x(6-x)[/tex]
[tex]72=2x^2+12x-x^2+6x-x^2[/tex]
[tex]x=\dfrac{72}{18}=4\ cm[/tex]
Se poate rezolva si cu asemanari de triunghiuri.
