The dimensions of the garden to maximize the area are length + width = 60 and the maximum area is 900 ft².
A rectangular garden will be fenced on all four sides.
120 ft. of fencing is available, what should be the dimensions of the garden to maximize the area and What is the maximum area to be determined.
The rectangle is a four-sided polygon whose opposites sides are equal and has an angle of 90° between its sides.
The perimeter of the rectangle = 120
Perimeter = 2 (length + width)
120 =2(length + width)
length + width = 120/6
length + width = 60 - - - -(1)
So, the sum of the sides of the rectangle should not increase by 120.
Now, the Maximum area of a rectangle,
Let Length = width
Equation 1
Length + Length = 60
length = 60/2
length = 30 = width
Area of the rectangle = length * width
= 30 * 30
= 900 ft²
So the maximum area of the rectangle is 900ft²
Thus, the dimensions of the garden to maximize the area is length + width = 60 and maximum area is 900 ft².
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