(related to Problem: A Problem in Squares)
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 $\frac{113}{120}$, $\frac{337}{120}$, $\frac{463}{120}$; and with a common difference of $13$ are $\frac{80929}{19380}$, $\frac{106921}{19380}$, and $\frac{127729}{19380}$. 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.
This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this edition or online at http://www.gutenberg.org. If you are not located in the United States, you'll have to check the laws of the country where you are located before using this ebook.
