Chapter 3.4, Problem 7AYU

(a)

To determine

To calculate:

Area of rectangle as function of width $w$ of rectangle

Answer to Problem 7AYU

The area $A$ of the rectangle as a function of the width $w$ of the rectangle is $-w^2+200w$ .

Explanation of Solution

Given Information:

  $400$ yards of fencing area.

Calculation:

A field is in the shape of rectangle.

Let the width of the rectangular field be $w$ and the area of rectangular is $A$

  $A=l\times w\Rightarrow A=\left(-w+200\right)w\Rightarrow A=-w^2+200w$

Hence, the area is $-w^2+200w$ .

(b)

To determine

To calculate:

The value of $w$ .

Answer to Problem 7AYU

The value of $w$ is the area largest is $100yd$ .

Explanation of Solution

Given Information:

  $400$ yards of fencing area.

Calculation:

A field is in the shape of rectangle.

Let the width of the rectangular field be $w$ and the area of rectangular is $A$

  $\frac{-b}{2a}=\frac{-200}{2\left(-1\right)}\Rightarrow 100yd$

Hence, value of $w$ is $100yd$ .

(c)

To determine

To calculate:

The maximum area.

Answer to Problem 7AYU

The maximum area is $10,000y{d}^2$ .

Explanation of Solution

Given Information:

  $400$ yards of fencing area.

Calculation:

A field is in the shape of rectangle.

Let the width of the rectangular field be $w$ and the area of rectangular is $A$

  $A=-{\left(100\right)}^2+200\left(100\right)\Rightarrow 10,000y{d}^2$

Hence, the maximum area is $10,000y{d}^2$ .