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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.
The above equation is in the form of a quadratic equation .
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
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