To find the maximum area of a rectangular field that can be enclosed and separated by a fence.
Answer to Problem 13P
The maximum area of the rectangular field enclosed by a fence is 26666.666 m2.
Explanation of Solution
Given information:
A rectangular field is enclosed by a fence and divided into two parts by another fence. The field is enclosed and separated with 800 m of fencing.
Let, the vertical and horizontal length of the fence around a rectangular field are
So, the total length of the fence
According to the question,
So, the horizontal length of the fence is
According to the given figure,
The horizontal length of the fence
The vertical length of the fence
The standard form of a quadratic equation:
So, the formula of the axis of symmetry:
Now, comparing the area of the rectangular field with the standard form of the quadratic equation:
By applying the formula of the axis of symmetry:
Hence,
The maximum area of the rectangular field enclosed by a fence is 26666.666 m2.
Chapter 7 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
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