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.


Anonymous said...

ok, what's going on here?

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

What's making this happen?


Anonymous said...

the answer is golden ratio

tenzin said...

how can AED possibly equal to BEF ?

are of triangle are equal ? thats impossible

Pat's Blog said...

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.

meera said...