To find: The largest area of rectangular plot of farmland enclosed by a single-strand electric fence and its dimension.
Answer to Problem 9E
The dimension of the fence is 400 m by 200 m.
The largest area of the plot is
Explanation of Solution
Given information: The length of the wire is given by 800 m.
Formula used:
Area of the rectangle,
Perimeter of the rectangle,
Calculation:
Suppose a and b be the sides of the rectangular fence.
Since, one side of the farmland is bounded by a river.
So, by considering only three sides, the perimeter will be,
The perimeter should be 800 m.
Thus,
Also, the area of the rectangle,
Taking the first derivative,
Assume
Thus,
Thus, the dimension will be
The largest area of the rectangular plot is given by,
Hence, the largest area of rectangular plot of farmland is 80,000 square meters.
Chapter 4 Solutions
Advanced Placement Calculus Graphical Numerical Algebraic Sixth Edition High School Binding Copyright 2020
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