WakeUp wrote: A rectangle can be divided into $n$ equal squares. The same rectangle can also be divided into $n+76$ equal squares. Find $n$. The ratio between sides of two squares must be a rational $\frac pq$ and we get $\frac{n+76}n=\frac {p^2}{q^2}$ And so $p^2-q^2=\frac{76}d$ where $d$ is a positive divisor of $76$ The only possible values for $d$ are $1,4$ and both give the solution $\frac pq=\frac{10}9$ and so $\boxed{n=324}$

How did you get $ \frac{n+76}{n}=\frac{p^2}{q^2} $ ?

let the side be ${p}$ of frist kind of squares and let ${q}$ be the side of the second kind of squares . so the ares of the rectangle =$n{p^2}=(n+76){q^2}$...now you can finish it !!