Final answer:
To find the length and width of the rectangular playground, we can use factors to solve a quadratic equation. The solutions indicate that the length is 5 yards and the width is 20 yards. The correct option is A.
Step-by-step explanation:
To determine the length and width of the rectangular playground, we can use factors to solve the problem.
Let's assume that the length of the playground is x yards. According to the problem, the width is 15 yards longer than the length, so the width would be (x + 15) yards.
Given that the surface area is 100 square yards, we can set up the equation: x(x + 15) = 100.
Simplifying this quadratic equation, we have x^2 + 15x - 100 = 0.
We can factorize this equation as (x + 20)(x - 5) = 0.
Therefore, the solutions to the equation are x = -20 and x = 5.
Since the dimensions of a playground cannot be negative, the length of the playground is 5 yards and the width is 5 + 15 = 20 yards.
Therefore, the correct answer is:
- Length = 5 yards
- Width = 20 yards