NOTE: I reposted this in Advanced Geometry before realizing there was a "Go Advanced" button here for doing that. I'll leave this open here for now but I think it's a more difficult problem than I first thought...

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).

I'm looking for the width (linedc) of this rectangle when the height (linede) 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 angleabcis 90 degrees. Also note that lineecis a diagonal of the rectangle from the lower left corner to the upper right corner and lineafruns from the middle of linedcto the lower right corner (f).

Just from experimenting a bit I know that line dc isabout7.1 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.