jmc

If the width of the rectangular playground is $w$, then the length is $2w+25$. A perimeter of 650 feet means the semi-perimeter is 325 feet. The width plus the length equals the semi-perimeter, so $w+2w+25=325$. That means $3w=300$, so $w=100$ feet. The length must be $2\times 100+25=225$. The area of the playground is $100\times 225=\boxed{22,500}$ square feet.