A rectangular backyard has a perimeter of 280 feet. The length of the backyard is 75 feet. What is the area of the backyard?
Let's label the width of the backyard as "w":
Perimeter = 2(length + width)
280 = 2(75 + w)
Dividing both sides by 2:
140 = 75 + w
Subtracting 75 from both sides:
65 = w
Now we have both the length and width of the backyard. To find the area, we simply multiply them:
Area = length x width
Area = 75 x 65
Area = 4,875 square feet
Therefore, the area of the rectangular backyard is 4,875 square feet.
To find the area of the rectangular backyard, we need to know its width. However, we can use the given information to find the width.
Let's assume the width of the backyard is represented by the variable "w." The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
Given that the perimeter is 280 feet and the length is 75 feet, we can substitute the values into the formula:
280 = 2 * (75 + w)
To solve for the width, we can start by simplifying the equation:
140 = 75 + w
Next, we can isolate the variable by subtracting 75 from both sides of the equation:
140 - 75 = w
Therefore, the width of the backyard is:
w = 65 feet
Now that we have both the length and width of the backyard, we can find the area using the formula:
Area = Length * Width
Substituting the values:
Area = 75 * 65
Therefore, the area of the backyard is:
Area = 4875 square feet