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 playground, we first need to find the dimensions of the rectangle.
Let's assume the width of the playground is "W" yards.
According to the given information, the length of the playground is 1.5 yards longer than its width, which can be expressed as:
Length = Width + 1.5
The perimeter of a rectangle is given by the formula:
Perimeter = 2(Length + Width)
Using the given perimeter of 40 yards, we can substitute the values into the perimeter formula and solve for the dimensions:
40 = 2(Length + Width)
40 = 2((Width + 1.5) + Width)
40 = 2(2Width + 1.5)
40 = 4Width + 3
37 = 4Width
Width = 37/4
Width = 9.25 yards
Now, we can find the length:
Length = Width + 1.5
Length = 9.25 + 1.5
Length = 10.75 yards
The dimensions of the playground are Width = 9.25 yards and Length = 10.75 yards.
To find the area of the playground, we use the formula:
Area = Length * Width
Area = 10.75 * 9.25
Area = 99.4375 square yards
Therefore, the area of the playground is 99.4375 square yards.
To find the area of the rectangular playground, we need to first determine the dimensions of the rectangle. We are given two pieces of information:
1. The perimeter of the playground is 40 yards.
2. The length of the playground is 1.5 yards longer than its width.
Let's denote the width of the rectangle as "w" yards. Since the length is 1.5 yards longer than the width, the length can be expressed as "w + 1.5" yards.
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width)
Using this formula and the given information, we can write the equation:
40 = 2((w + 1.5) + w)
Now, we can solve this equation to find the width "w":
40 = 2(2w + 1.5)
40 = 4w + 3
4w = 40 - 3
4w = 37
w = 37/4
w ≈ 9.25
Now that we have the value of the width, we can find the length:
Length = Width + 1.5
Length ≈ 9.25 + 1.5
Length ≈ 10.75
So, the width is approximately 9.25 yards and the length is approximately 10.75 yards.
Finally, to find the area of the playground, we use the formula: Area = Length × Width
Area ≈ 9.25 × 10.75
Area ≈ 99.4375
Therefore, the area of the rectangular playground is approximately 99.4375 square yards.