Therefore the the length =21 and width =42 of the plot that will maximise the area is 882 [tex]ft^{2}[/tex] .
A region's size on a planar or curved surface can be expressed mathematically as its area. The term "surface area" refers to the area of a surface or the border of a three-dimensional object, whereas the term "plane area" refers to the area of a shape or planar lamina.
Here,
Here, take note that the shape is still a rectangle and the fencing is still 84 feet long.
As a result, the area is equal to xy and the sum of the sides NOT along the river is 84.
Thus, 2x + y = 84 and A = xy are the two equations.
We must find A as a function of x or y to determine the area with the largest value. My recommendation is to solve the first equation for y and substitute that value into the second equation.
A(x) = x and y = 84 - 2x (84-2x)
Currently, we must maximize A(x) = 84x - 2.
Recall that if we determine the vertex's x value by substituting, x = -b/(2a), we may find the vertex's y value.
Therefore, x = -84/(-4) = 21 ft because a = -2 and b = 84. If x = 21, y = 84 - 2(21) = 42
Thus, the dimensions are 21 by 42, and the maximum size is 21 by 42, or 882 square feet.
Therefore the the length =21 and width =42 of the plot that will maximise the area is 882 [tex]ft^{2}[/tex] .
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