(1) The area of the inscribed square in the ellipse $\frac{x^{2}}{5^{2}}+\frac{y^{2}}{3^{2}}=1$ is
(1) $\frac{450}{17}$ Hint: According to the symmetry of the ellipse, the sides of the inscribed square should be parallel to the coordinate axes, and the center should be at the origin, so the equations of its diagonals are $y= \pm x$. Substituting into the ellipse equation gives $x^{2}\left(\frac{1}{5^{2}}+\frac{1}{3^{2}}\right)=1$, then $S=(2 x)^{2}=\frac{450}{17}$.