John wants to build a corral next to his barn. He has 300 feet of fencing to enclose three sides of his rectangular yard. a. What is the largest area that can be enclosed? b. What dimensions will result in the largest yard?
Accepted Solution
A:
Let's first define the variables: x = width 300 - 2x = long The area will be: A = (x) * (300 - 2x) A = 300x - 2x² We look for the maximum area, for this, we derive: A '= 300 - 4x We match zero: 0 = 300 - 4x x = 300/4 = 75 Therefore, the width is: x = 75 feet The length is: 300 - 2x = 300 - 2 (75) = 300-150 150 feet Answer: Part A: The maximum area will be: A = (150) * (75) = 11250 square feet Part B: The dimensions are: Length = 150 feet width = 75 feet