Question

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

The maximum area of kennel is $1800{\text{ft}}^2$.

Step-by-step solution

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

Step 2. Use the concept.

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

Consider the function $f\left(x\right)=a{x}^2+bx+c,a\ne 0$, the x-coordinate of vertex is $\frac{-b}{2a}$.

The graph of $f\left(x\right)=a{x}^2+bx+c,a\ne 0$

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

Step 3. Solution.

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

So, the maximum area of kennel is

$\begin{array}{l}\text{Area}=\text{length}\cdot \text{width}\\ \Rightarrow A=30\cdot 60\\ \Rightarrow A=1800{\text{ft}}^2\end{array}$

So, the maximum area of kennel is $1800{\text{ft}}^2$