[SOLVED] finding the aspect ratio of a rectangle

[I originally posted this as a HS level geometry problem but I'm now thinking it's more difficult than that.]

It's been too long since I've had to figure something like this out. I'm hoping someone will be kind enough to help. I'm attaching a picture of what I'm working on as it will make it easier to describe. (I'll leave the image up until someone's given me an answer).

http://farm4.static.flickr.com/3422/...bbb266d55b.jpg

I'm looking for the width (line *dc*) of this rectangle when the height (line *de*) is 5 inches (and for the formula needed to figure it out). Note that the blue line (*da*) and red line (*ac*) are equal in length and that angle *abc* is 90 degrees. Also note that line *ec* is a diagonal of the rectangle from the lower left corner to the upper right corner and line *af* runs from the middle of line *dc* to the lower right corner (*f*).

Just to clarify:

- Point
*a* must bisect line *dc*. - Angle
*abc* must be 90 degrees. - Points
*e*, *c* and *f* must be in their respective corners.

From experimenting a bit I know that line *dc* is *about* 7.1 inches. I'd like the formula for getting the exact length.

Thank you in advance. I didn't think this would be that hard to figure out but I don't really know how to even approach solving it.