Tiffany is constructing a fence around a rectangular tennis court. She must use 300 feet of fencing. The fence must enclose all four sides of the court. Regulation states that the length of the fence enclosure must be at least 80 feet and the width must be at least 40 feet. Tiffany wants the area enclosed by the fence to be as large as possible in order to accommodate benches and storage space. What is the optimal area?
You want the max area, which is 75*75. But, the length must be 80. making it as close as possible, 80*70= 5600
5600 square feet
To find the optimal area, we need to determine the dimensions of the tennis court that will maximize the area while still meeting the given conditions.
Let's assume the length of the tennis court is represented by "L" and the width is represented by "W".
We are given that the length of the fence enclosure must be at least 80 feet. So we have:
2L + W = 300 -- (Equation 1)
We are also given that the width of the fence enclosure must be at least 40 feet. So we have:
L + 2W = 300 -- (Equation 2)
To find the optimal area, we need to solve these equations simultaneously.
Let's start by solving Equation 1 for W:
W = 300 - 2L
Now substitute this value of W into Equation 2:
L + 2(300 - 2L) = 300
Simplify:
L + 600 - 4L = 300
Combine like terms:
-3L = -300
Divide both sides by -3:
L = 100
Substitute the value of L back into the equation of W:
W = 300 - 2(100)
W = 100
So, the optimal dimensions for the tennis court are a length of 100 feet and a width of 100 feet.
Now, to find the optimal area, we multiply the length and width:
Area = L * W
Area = 100 * 100
Area = 10000 square feet
Therefore, the optimal area enclosed by the fence is 10000 square feet.
To find the optimal area, we need to determine the dimensions of the court that will maximize the enclosed area. Let's assume the length of the court is represented by 'L' and the width is represented by 'W'.
We know that the length of the fence enclosure must be at least 80 feet, so we can write the equation: L ≥ 80.
Similarly, the width of the fence enclosure must be at least 40 feet, so we can write the equation: W ≥ 40.
Now, we need to consider the perimeter of the court. Since the fence must enclose all four sides, the perimeter is the sum of the length and width multiplied by 2: 2L + 2W.
We also know that the total length of fencing available is 300 feet, so we can write another equation: 2L + 2W = 300.
To find the optimal area, we can substitute the value of 2L + 2W from the second equation into the equation for the area, which is A = L * W.
Area (A) = L * W
Substituting the value of 2L + 2W from the second equation:
A = (300 - 2W) * W
Now we have an equation for the area in terms of W. We can find the maximum area by finding the value of W that maximizes the equation.
To do this, we can take the derivative of A with respect to W, set it to zero, and solve for W.
the maximum possible area would be a square, 75x75. But, since the length must be at least 80, make it as close to a square as possible. That would be
80x70