Rectangle Area Puzzle

Feb 2018
21
1
California
Hello! Trying to figure out this question: Find the dimensions of a rectangle such that each side is a non-integer, but the area is an integer. How could this be possible? Any hints or solutions welcome. Thank you!
 
Jun 2019
493
261
USA
Many ways this could be possible. Design a rectangle with an area of $1~in^2$, with one side being $\displaystyle \frac{3}{2}~in$. What is the length of the other side?
 

mathman

Forum Staff
May 2007
6,895
760
Even better - irrationals. One side $\pi$ and the other side $\frac{1}{\pi}$. Area $=1$.
 
Nov 2018
21
0
Iran
Or having one side $\sqrt{2}$ and the other side $ \sqrt{8} $ the area will be $\sqrt{16}=4$