Respuesta :
Answer:
The dimensions of the rectangular area are 15 ft and 30 ft.
Step-by-step explanation:
Consider the provided information.
Cesar wants to fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. He has 60 feet of fencing available.
We need to find the dimensions that will enclose the maximum area.
Let the length of the fence is x feet.
Let the width of the fence is y feet.
The total fencing available is 60 feet.
Thus, width is: y = 60 - x - x = 60 - 2x
The area of rectangle is = length×width
The area of rectangle is = (x)×(60 - 2x)
A = 60x - 2x²
The above function opens downwards as the coefficient of x² is a negative number, thus the maximum of the function can be calculated as:
x max = -b/2a
In the above function a = -2 and b = 60
Substitute the value of a and b in x max = -b/2a
x max = -60/-4 = 15 feet
Thus the value of x is 15, now calculate the value of y as shown:
y = 60 - 2x
y = 60 - 30
y = 30
Hence, the dimensions of the rectangular area are 15 ft and 30 ft.
