The diagram at the left is the left half of the design for a general  pyramiddle tent. Four right triangles divide the entire space.   

    h is the height of the finished tent and is also half the width of the tarp from which the tent is constructed. 

    d is the width of one door flap and half the width of the finished tent (z is the depth of the finished tent.) 

    r is the depth of the tarp used to create the tent.
 

-- Making liberal use of the Pythagorean Theorem, the four right triangles give the equations at the right.

-- The idea was then to solve for d in terms of h and r. This would let me design a pyramiddle tent from nearly any rectangular tarp.

-- After hours of trying, I found that I could not get anywhere with the solution, and so I just wrote a computer program to try every value of d for a given h and r, and to report the correct solution. This gave me answers, but did not solve this interesting math problem.

Can you solve the problem? Just figure out an equation that
yields d when values for h and r are inserted?

My little computer program gives the following results, which you can use to check your solution of the problem. The values of d may not be quite precise, but are very close:
h                    r                     d
72                 108                  36
72                 136                  29
50                   72                  26
60                   70                  40

Here is how I solved the problem. If figured that the internet can answer any question, if it is presented correctly. So, first I made this web page explaining the problem.
Then, I went a-browsing for algebra sites. Within each that I found, I looked for an email address, and sent a plea for help along with a link to this page. Sure enough, in less that 24 hours I had solutions from two different sources.

Theo Monahos at the Personal Algebra Tutor site was first in with a fax.
Dr. Rick at the Ask Dr. Math site sent me email just hours later with the same solution. 

The final equations can be found elsewhere on these Tarp Tent pages, but I will keep the problem posted here for all of you folks that love a little math puzzle.