Final answer:
The length of the rectangular playground can be found by setting up an equation using the perimeter. The width is found to be 102 feet and the length is found to be 219 feet. The area of the playground is 22,338 square feet.
Step-by-step explanation:
To find the area of the rectangular playground, we need to use the given information. Let's start by assigning variables to the width and length of the playground. Let's say the width is 'w' feet. According to the problem, the length exceeds twice the width by 15 feet. So the length would be '2w + 15' feet.
The perimeter of a rectangle is given by the formula 2(length + width). In this case, the perimeter is given as 540 feet. So we can write the equation as 2(2w + 15 + w) = 540. Simplifying this equation, we get 5w + 30 = 540. Solving for 'w', we find that the width is 102 feet.
Now, we can plug this value back into the expression for the length to find the length of the playground. Length = 2(102) + 15 = 219 feet.
The area of a rectangle is given by the formula length x width. So the area of the playground is 102 feet x 219 feet = 22,338 square feet.