Let's call the length of the rectangular field x and the width y.
According to the problem, the total amount of fencing the farmer has is 2400 ft.
The fencing consists of two lengths and two widths: 2x + 2y = 2400.
Dividing this equation by 2 gives: x + y = 1200.
Now, we want to maximize the area of the field, which is given by A = x * y.
To find a function that models the area in terms of one of its sides, we can use the equation x + y = 1200 to express y in terms of x.
y = 1200 - x.
Substituting this into the area equation, we get A = x(1200 - x).
Simplifying, we have A = 1200x - x^2.
Now, we can find the maximum area by finding the x-value that corresponds to the vertex of the quadratic function A = 1200x - x^2.
The x-value of the vertex can be found using the formula: x = -b / (2a).
In this case, a = -1 (the coefficient of x^2) and b = 1200 (the coefficient of x).
Therefore, x = -1200 / (2*(-1)) = 600.
So, the dimension that maximizes the area is x = 600.
We can then find the corresponding y-value using the equation y = 1200 - x.
y = 1200 - 600 = 600.
Therefore, the dimensions of the field of largest area that the farmer can fence off are 600 ft by 600 ft.
A farmer has 2400ft of fencing and wants to fence off a rectangular field that borders a straight river he does not need a fence along the river what are the dimensions of the feild of largest area that he can fence
Experiment with the problem drawing several diagrams illustrating the situation calculate the area of each configuration and use your results to estimate the dimensions of target possible field enter your answer as a comma separated list
Find a function that models the area of the feild in terms of one of its sides
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