jmc

Call the greater of the two squares $x^2$. Because the squares are consecutive, we can express the smaller square as $(x-1{)}^2$. We are given that $x^2-(x-1{)}^2=35$. Expanding yields $x^2-x^2+2x-1=35$, or $2x=36$. Therefore, $x=18$, so the larger square is $18^2=\boxed{324}$.