Question

Chris wants to fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. He has
120
feet of fencing available. Find the dimensions that will enclose the maximum area.

The fence parallel to the house is ___
feet, the fence perpendicular to the house is ____
feet and the area of the yard is ____
square feet.

Answer 1

Answer:

• parallel: 60 ft
• perpendicular: 30 ft
• area: 1800 ft^2

Step-by-step explanation:

Let x represent the length of fence parallel to the house. Then the length perpendicular is ...

  y = (120 -x)/2

The area of the yard is the product of these dimensions, so is ...

  A = xy = x(120-x)/2

This is the equation of a parabola that opens downward and has zeros at x=0 and x=120. The maximum (vertex) is on the line of symmetry, halfway between these zeros, at x=60.

The fence parallel to the house is 60 feet.

The fence perpendicular to the house is (120-60)/2 = 30 feet.

The area of the yard is (60 ft)(30 ft) = 1800 ft^2.