Respuesta :
To find the dimensions of the parking lot, we can use the formula for the area and perimeter of a rectangle.
The area of a rectangle is found by multiplying its length and width, so we have:
Area = length * width
Given that the area of the parking lot is 4000 square yards, we can set up the equation as:
4000 = length * width
The perimeter of a rectangle is found by adding twice the length and twice the width, so we have:
Perimeter = 2 * length + 2 * width
Given that the perimeter of the parking lot is 260 yards, we can set up the equation as:
260 = 2 * length + 2 * width
Now, we have a system of equations:
4000 = length * width
260 = 2 * length + 2 * width
To solve this system, we can use substitution or elimination. Let's solve it using substitution.
From the second equation, we can isolate one of the variables. Let's solve for length:
260 = 2 * length + 2 * width
260 - 2 * width = 2 * length
130 - width = length
Substituting this value of length into the first equation, we get:
4000 = length * width
4000 = (130 - width) * width
Simplifying the equation, we have a quadratic equation:
4000 = 130w - w^2
Rearranging the equation, we get:
w^2 - 130w + 4000 = 0
Now, we can solve this quadratic equation to find the width of the parking lot. Once we have the width, we can substitute it back into the equation we found earlier to find the length.
Solving the quadratic equation, we get two possible solutions for the width: w = 80 or w = 50.
If we choose w = 80, then substituting it back into the equation 4000 = (130 - width) * width, we get:
4000 = (130 - 80) * 80
4000 = 50 * 80
4000 = 4000
Therefore, if the width is 80 yards, the length is also 50 yards.
If we choose w = 50, then substituting it back into the equation 4000 = (130 - width) * width, we get:
4000 = (130 - 50) * 50
4000 = 80 * 50
4000 = 4000
Therefore, if the width is 50 yards, the length is also 80 yards.
In summary, the dimensions of the parking lot can be either 50 yards by 80 yards or 80 yards by 50 yards.
