Question

The area of a playground is 36 square yards. The length of the playground is 4 times longer than its width. Find the length and width of the playground.

Answer 1

The width and the length of the playground are found by setting up an equation based on the given area of 36 square yards and the fact that the length is four times the width, resulting in dimensions of 3 yards in width and 12 yards in length.

Step-by-step explanation:

The question involves finding the length and width of a playground where the area is 36 square yards, and the length is 4 times longer than its width.

Steps to Solve the Problem

1. Let w represent the width of the playground in yards.
2. Since the length is 4 times longer, let 4w represent the length of the playground in yards.
3. The area of a rectangle is calculated by multiplying the length by the width. Here, the area is given as 36 square yards.
4. Set up the equation w × 4w = 36 and solve for w.
5. Simplifying, we get 4w^2 = 36. Divide both sides by 4, which gives w^2 = 9.
6. Take the square root of both sides to find w, and we get w = 3 yards.
7. Now that we know the width, calculate the length by multiplying the width by 4: 4 × 3 = 12 yards.

Therefore, the playground's dimensions are 3 yards in width and 12 yards in length.