The perimeter of a rectangular playground is 40 yards. It is 1.5 yards longer that it is wide. What is area of playground?
To find the area of the rectangular playground, we first need to find the dimensions of the rectangle. Let's denote the width of the playground as "W" in yards.
According to the given information, the perimeter of the playground is 40 yards. The formula for the perimeter of a rectangle is: Perimeter = 2 * (Length + Width)
In this case, the length of the playground is 1.5 yards longer than its width, so we can express it as: Length = Width + 1.5
Substituting these values into the perimeter formula, we have: 40 = 2 * (Width + (Width + 1.5))
Simplifying the equation: 40 = 2 * (2 * Width + 1.5)
Further simplifying gives: 40 = 4 * Width + 3
Now, let's isolate the "Width" term: 4 * Width = 40 - 3
Simplifying: 4 * Width = 37
Finally, divide both sides of the equation by 4 to solve for the Width: Width = 37 / 4 = 9.25 yards
Now that we have the width, we can find the length by adding 1.5 yards to the width: Length = Width + 1.5 = 9.25 + 1.5 = 10.75 yards
The area of a rectangle can be calculated by multiplying the length and width: Area = Length * Width
Substituting the values we found: Area = 10.75 * 9.25 = 99.4375 square yards
So, the area of the rectangular playground is approximately 99.44 square yards.