Fencing a Garden A determined gardener has 120 ft of deer-resistant fence. She wants to enclose a rectangular vegetable garden in her backyard, and she wants the area that is enclosed to be at least 800 ft2. What range of values is possible for the length of her garden?
The range of values possible for the length of garden for fencing.
Answer to Problem 119E
The range of length of the garden for fencing is from
Explanation of Solution
The length of deer resistance fence is
Recall the fact that the value of perimeter of the garden will be equal to the length of the fence. That is,
Since the area of the rectangular vegetable garden is atleast
Note that, the perimeter of the rectangular vegetable garden is
Substitute
Substitute
Substitute
Simplify further as follows:
Solve further as follows:
Thus, the range of length of the garden for fencing is from
Chapter 1 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning