, 2026

Suppose that the side length of the original square is $x$. Since the original square has area
$10$, then $x^2=10$. The new square has side length
$kx$ where $k$ is a positive integer. The area of the
new square is $(kx)^2=k^2\times x^2=10k^2$. Consider setting $10k^2$ equal to each of the five choices
given and solving for $k$. Of these
five choices, $90$ is the only area
for which $k$ is a positive integer
($10k^2=90$ when $k=3$).