## Square with a hole

Instructions
PQR is a triangle [display]O\in PQR[/display] [display]d_1//PQ \wedge O\in d_1[/display] [display]d_2//QR \wedge O\in d_2[/display] [display]d_3//QR \wedge O\in d_3[/display] WHat's the ratio between the area of the 3 small triangles and PQR ? (Greyed in figure)
Dumy solution
Really, I don't know a dumy solution ! Please, give me one ;-)
Smart solution (click to open)
Look at diagrams bellow :
We appended the image of himself then skewed it a bit.
The side of each triangle is the square root of the area of each surface !
We get as answer: [display]\sqrt{S_{yellow}}+\sqrt{S_{blue}}+\sqrt{S_{green}}=\sqrt{S_{total}}[/display] Yep, this is a rectangle and I use square root to find the side !
But's because rectangle and square differ only by length.