perplexus.info :: Geometry : Sharing a Plot

Sharing a Plot (Posted on 2004-08-05)

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.

Submitted by Brian Smith

Rating: 2.8000 (5 votes)

Solution: (Hide)

Since the outer edge of each person's triangle is in proportion to the area they each recieve, the common vertex is the same distance from all three sides of the large triangle, ie the point is the incenter of the triangle.
Incenter radius = Area/semiperimeter = (30*40/2)/((50+40+30)/2) = 10. Thus, coordinates are (10,10).

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
answer	K Sengupta	2007-11-16 04:50:55
Solution	Rajal	2004-08-05 09:56:09
soln	neshal	2004-08-05 09:42:53
Quick	Oskar	2004-08-05 08:24:56

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