The maximum value of the area that can be enclosed by edging will be 20,000 feet.
The area is a amount of space within the perimeter of a two dimensional space.
Area = length × breadth
Minimum or maximum value:
The minimum or maximum value of a quadratic is given by the value of the function at the vertex.
According to the given question
We have
400feet of edge material to surround three side.
Suppose length one side of the rectangular yard is y feet
and, x be the length other two sides.
⇒ y + 2x =400
⇒ y = 400 - 2x
Therefore,
Area = x × y = x(400 -2x)
Area = 400[tex]x[/tex] - [tex]x^{2}[/tex]
the graph of the area will be parabola
for the vertex of the parabola
x = [tex]\frac{-400}{-4}[/tex] = 100 ( for vertex of parabola, x = [tex]\frac{-b}{2a}[/tex] and f(x))
⇒ the area will maximum at x = 200 feet.
so,
the maximum area = (100)(400 -200)
the maximum area = 100×200 = 20,000 square feet.
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