To find the dimensions of the field with the largest area that can be fenced, let's assume the length of the field is x feet.
Since the field is rectangular, we can divide the available fencing into 3 sides: two sides of length x feet each and one side along the river. The total length of these three sides should add up to 2400 feet, which gives us:
2x + river side = 2400
river side = 2400 - 2x
To find the area of the field, we use the formula: A = length * width. Since the width is the side opposite the river, it will be the remaining side of length x feet:
A = x * (2400 - 2x)
A = 2400x - 2x^2
To find the maximum area, we need to find the critical point of this quadratic equation by taking its derivative and setting it to zero:
A'(x) = 2400 - 4x = 0
4x = 2400
x = 600
So, the length of the field should be 600 feet. The width would be the remaining side, which is (2400 - 2x) = (2400 - 2*600) = 1200 feet.
Therefore, the dimensions of the field with the largest area that can be fenced are 600 feet by 1200 feet.
The function that models the area of the field in terms of one of its sides x is:
A(x) = 2400x - 2x^2
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
A(x)
1 answer
1 answer