Respuesta :
Dimension of maximize area is, length = 1581 m and breadth = 790.5 m.
Given that a rectangular plot of land adjacent to a river is to be divided into two equal plots. And 3162 ft of fencing to enclose the plot.
Consider the length is L and breadth is B of the plot.
Therefore the perimeter = L + 2B = 3162
⇒ L = 3162 - 2B
We know that area is the product of length into breadth i.e,
Area = L × B
= (3162 - 2B) × B
Area = 3162B - 2B²
The maximum of the quadratic expression is
ax² + bx + c is at s = [tex]\frac{-b}{2a}[/tex] if a < 0.
Now we will calculate maximum point of the equation,
B = [tex]\frac{-3162}{2(-2)}[/tex]
B = 790.5
Now we will find the value of length,
L = 3162 - 2B
= 3162 - 2(790.5)
= 3162 - 1581
L = 1581
Hence the length of the rectangular plot is 1581 m and bredth is 790.5 m.
Therefore the maximize area = 1581 × 790.5 =124978
To know more about area here
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