Solution: Let the sides be $ a $ and $ b $. By the Pythagorean theorem, $ a^2 + b^2 = 25^2 = 625 $. The area $ A = ab $. To maximize $ A $, use the identity $ (a + b)^2 = a^2 + 2ab + b^2 $, but it is more direct to note that for fixed $ a^2 + b^2 $, $ ab $ is maximized when $ a = b $. Thus, $ 2a^2 = 625 \Rightarrow a = rac25\sqrt2 $. The maximum area is $ A = \left(rac25\sqrt2 - Veritas Home Health