Sam Loyd's Geometric Puzzle (S462b)
From: Interactive Mathematics Miscellany and Puzzles
From Mathematical Puzzles of Sam Loyd selected and edited by Martin Gardner (Dover, 1959), came puzzle #36. The puzzle is framed into a story of an auction at which a plot of land comprising three squares surrounding a triangular lake was offered for sale. Sam Loyd states the puzzle thus:
The question I ask our puzzlists is to determine how many acres there would be in that triangular lake, surrounded as shown by square plots of 370, 116 and 74 acres. The problem is of peculiar interest to those of a mathematical turn, in that it gives a positive and definite answer to a proposition which, according to usual methods, produces one of those ever-decreasing, but never-ending decimal fractions.
If you give up and want the solution