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Chapter 6: Q50. (page 292)

Steve has 120 feet of fence to make a rectangular kennel for his dogs. He will use his house as one side. Find the maximum area of the kennel.

Short Answer

Expert verified

The maximum area of kennel is 1800ft2.

Step by step solution

01

Step 1. Given Information.

Steve has 120 feet of fence. He uses his house as one side.

Let

w = width of house

l = length of kennel

02

Step 2. Use the concept.

The y-intercept is the point where the graph intersects they-axis.

Consider the function f(x)=ax2+bx+c,a≠0, the x-coordinate of vertex is -b2a.

The graph of f(x)=ax2+bx+c,a≠0

  • opens up and has a minimum value when a>0, and
  • opens down and has a maximum value when a<0
03

Step 3. Solution.

The dimensions that produce maximum area should be 30 ft and 60 ft.

So, the maximum area of kennel is

Area=length⋅width⇒A=30⋅60⇒A=1800ft2

So, the maximum area of kennel is 1800ft2

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