Problem  of the  Week

A field in the shape of a right triangle is to be subdivided into two fields of equal size by building a straight fence between two sides of the field.  If the lengths of the sides of the field are 300 and 400 feet long, respectively, with the hypotenuse being 500 feet long, what is the shortest fence that will do the job and where should the fence be built?

For the more adventurous:  Solve the same problem for a right triangular field of arbitrary dimensions.

For the thrill seeker:  Solve the same problem for a triangular field of arbitrary shape.

A puzzler:  For each letter of the English alphabet, find a word which contains that letter as a double letter.  To get you started, the word LETTER contains the letter T as a double letter.  Now find the other letters.  Of course, some words contain two double letters.  Bonus points for finding the fewest number of words which exhibit the most total double letters. Demerits will be given for using proper names! I don't know any words that contain triple letters; does anyone know one?

For our overseas friends:  Feel free to use your native language!  I'd especially like to see what you come up with in Español, Deutsch, and Français -- in these languages the puzzler is much harder!