Bermuda Tarpezoid Challenge Problem

[shaji]

"If triangle ABC has twice the area of trapezoid ADEC, then triangle ABC must also have twice the area of triangle DBE (look at the diagram: each of these smaller areas comprise half the area of large triangle ABC). - INCORRECT

"Triangle ABC and Triangle DBE are similar"-INCORRECT

The solution is flawed.

Please clarify

[tim]

Good suggestion. Can you please clarify what you think is wrong here? Also, be sure to post the entire text of the problem so other students can benefit from our discussion.

[shaji]

Thanks Tim

The text of the problem. Sorry! about the diagram. Restriction on pasting images in this forum.

Last Week's Problem: "The Bermuda Trapezoid Triangle

Triangle ABC is cut by a line DE parallel to side AC, as shown in the diagram. If side AC has length 1, and the area and perimeter of triangle ABC are both twice the corresponding values for trapezoid ADEC, what is the perimeter of triangle DBE?
Answer This Week's Question for Prize

First the most obvious, the 2nd Point. Prove how Triangle ABC is similar to Triangle DBE.


In the absence of the diagram, 1st Point is difficult to visualise.

[shaji]

Since the diagram can't be shown, I comment as follows:

The solution is correct if and only if points D & E lie on lines BA & BC respectively. The diagram shows points D & E outside triangle ABC, and if so, the solution is flawed.

[RonPurewal]

this is probably rather obvious at this point, but, you're going to have to post the diagram if this conversation is to have any chance of proceeding profitably.

if the image is on the web, you can embed it in your post. (just click the "img" button above the post while you are writing, and the formatting will be done automatically.)

if it's on your own computer, then upload it to a site such as postimage.org and then post a link.

thanks.

[shaji]

Thanks Ron

The link of the image for all to see.

http://www.manhattangmat.com/images/Cha ... rmuda1.gif

I repeat for all to note:-

The solution is correct if and only if points D & E lie on lines BA & BC respectively. The diagram shows points D & E outside triangle ABC, and therefore, the solution is flawed.

[RonPurewal]

ah, yes, i think those points are supposed to be on the triangle. i'll pass on the word, thanks.