The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.
It is a polygon with four sides. The total interior angle is 360 degrees. A rectangle's opposite sides are parallel and equal, and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
Marquise has 200 meters of fencing to build a rectangular garden.
The garden's area (in square meters) as a function of the garden's width x (in meters) is modeled by:
A(x)= - x² + 100x
The perimeter of the rectangle = 2( length + Width)
200 = 2( length + Width)
100 - x = L
The area of the rectangle = length × Width
= x(100 - x)
= (-x)²+ 100x
So, (-x)²+ 100x where, a = -1 and b = 100
w = -100/2(-1)
w = 50
The area of the rectangle = (-x)²+ 100x
= (-50)²+ 100(50)
= 2500
Thus, The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.
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