To find: the bounds for the length of the rectangle.
Answer to Problem 79E
Explanation of Solution
Given:
The rectangular field has perimeter 100 m. Its area should be at least 500 square meters.
Concept Used:
Quadratic Formula:
The zeros of the polynomial
Let L denotes the length of the rectangle and W denotes the width of the rectangle.
Perimeter = 100 m
Now, area of the rectangle is,
It is required that area must be at least 500 square meters. That is,
First step to solve the given inequality is to find the key numbers of the inequality. For that, find zeros of the polynomial
Thus, the key numbers are
Since length is always greater than 0.
So, the inequality’s test intervals are
In each test interval, choose a representative x -value and evaluate the polynomial.
Test-Interval | x -value | Polynomial Value | Conclusion |
Positive | |||
Negative | |||
Positive |
The inequality is satisfied for all x -values in
This implies that the solution set of the inequality
Conclusion:
So, for the rectangular field to have area at least 500 square meters, the bound on its length should be
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
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