Tuesday, 13 October 2009

An Interesting Geometry Problem


Came across a geometry problem with an interesting result which I did not suspect... thought I would share...
In the figure, rectangle ABCD is inscribed with a triangle by selecting points E and F on the segments AB and BC respectively, so that triangles AED, BEF, and CFD all have equal area. Find the ratios of AE:EB and BF:FC. I was surprised, and pleased, hope you are as well.
at

5 comments:

  1. Anonymous19 October 2009 at 04:36

    ok, what's going on here?

    I recalculated with some actual numbers to make sure I hadn't goofed.

    What's making this happen?

    Jonathan

    ReplyDelete
  2. Anonymous22 November 2009 at 10:58

    Wow!!!
    the answer is golden ratio

    ReplyDelete
  3. tenzin4 November 2011 at 19:29

    how can AED possibly equal to BEF ?

    are of triangle are equal ? thats impossible

    ReplyDelete
  4. Pat's Blog4 November 2011 at 20:37

    Tenzin, just like in the textbook, triangles are not (necessarily) drawn to scale. Your job is to find the locations of points E and F that make the equality happen. Try again.

    ReplyDelete
  5. meera13 August 2013 at 15:04

    ((6^(1/2))-1)/2

    ReplyDelete