Question

John wants to build a corral next to his barn. He has 300 feet of fencing to enclose three sides of his rectangular yard.

Answer 1

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