Respuesta :
Answer:
The dimensions of is width: 41, length: 82
Step-by-step explanation:
Consider the provided information.
Let y is the length of side parallel to the wall  and x is length of each side perpendicular to the wall.
The perimeter of rectangle is 2x + 2y since, we need to use the side of building and fencing for the other 3 sides. Therefore,
y + 2x = 164
y = 164-2x
The area of rectangle is xy.
[tex]A = xy = x(164-2x) [/tex]
[tex]A = -2x^2+164x[/tex]
The above equation is in the form of a quadratic equation [tex]ax^2+bx+c=0[/tex].
The graph of the function is a parabola opening downward. As the coefficient of x² is negative. The maximum occurs at the x-coordinate of the vertex.
In order to find the vertex, use the formula [tex]x=\frac{-b}{2a}[tex] and substitute the value of x in above equation.
x = -164/(2(-2)) = 41
Now substitute x = 41 in [tex]A = -2x^2+164x[/tex]
[tex]A = -2(41)^2+164(41)[/tex]
[tex]A = -2(1681)+6724[/tex]
[tex]A = -3362+6724[/tex]
[tex]A = 3362[/tex]
So the vertex is (41,3362).
This shows us that the max area is then 3362 square feet.
Now substitute the value of x in y = 164-2x
y = 164-2(41)=82
Hence, the dimensions of is width: 41, length: 82
