Question

The surface are covered by a rectangular playground is 100 square yards. the width of the playground is 15 yards longer than it’s length. using factors, determine the length and the width of the playground:

A) Length = 5 yards, Width = 20 yards

B) Length = 10 yards, Width = 25 yards

C) Length = 15 yards, Width = 30 yards

D) Length = 20 yards, Width = 35 yards

Answer 1

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