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?

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
 
 Part A:
 The maximum area will be:
 A = (150) * (75) = 11250 square feet
 Part B:
 The dimensions are:
 Length = 150 feet
 width = 75 feet