251. At the base of a quadrilateral pyramid lies a rectangle, one side of which is equal to $a$, the lateral edges of the pyramid are equal to $b$. Find the maximum value of the volume of such pyramids.
251. If $x$ is the length of the two other sides of the rectangle, then the volume of the pyramid is $\frac{a x}{3} \sqrt{b^{2}-\frac{a^{2}}{4}-\frac{x^{2}}{4}}$. The maximum volume will be when $x=\sqrt{\frac{4 b^{2}-a^{2}}{2}}$, and it is equal to $\frac{a\left(4 b^{2}-a^{2}\right)}{12}$.