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.

Area of entire plot: 0.5*40*30=600

600/(5+4+3)=50

Carl's portion = 3*50 = 150

Shortest side is 30: 0.5*30*h=150 => h=10

Middle side is 40: 0.5*40*h=200 => h=10

Answer is 10,10

Note that Alex's plot has h=10 as well and the prices match their area - someone's giving hints

Posted by Rajal on 2004-08-05 09:56:09