MATH SOLVE

4 months ago

Q:
# 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

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