237. $\left\{\begin{array}{l}x+y+\sqrt{x^{2}+y^{2}}=\frac{x y}{2} \\ x y=48 .\end{array}\right.$
237. $x+y+\sqrt{x^{2}+y^{2}}=24 ; \sqrt{x^{2}+y^{2}}=24-(x+y)$.

By squaring, we find: $x+y=14$; then by the sum and product, we find $x=8$ and $y=6$.