The sides of the three boards measure 31 in., 41 in., and 49 in. The
common difference of area is exactly five square feet. Three numbers
whose squares are in A.P., with a common difference of 7, are 113/120,
337/120, 463/120; and with a common difference of 13 are 80929/19380,
106921/19380, and 127729/19380. In the case of whole square numbers the
common difference will always be divisible by 24, so it is obvious that
our squares must be fractional. Readers should now try to solve the case
where the common difference is 23. It is rather a hard nut.