Alex, Bert and Carl contributed $250, $200 and $150 respectively toward the purchase of a triangular plot. They'd like to divide the land into three smaller triangles such that the ratios of the areas are 5:4:3 (the ratio that they paid).

Alex wants to own the longest side, Bert the second longest, and Carl the shortest. Their three triangles meet at a shared central point.

Given that the vertices of the triangle lie at (0,0), (0,30), and (40,0). Find the coordinates of that point.

The area of the triangle is 600, so A gets 250, B 200 and C 150. C gets the 30 side, so the height of his triangle must be 10. B gets the 40 side, so the height of his triangle must also be 10. Therefore, the coordinates of the central point are (10,10).

Posted by Oskar on 2004-08-05 08:24:56