Chapter 8.3, Problem 32PPS

(a)

To determine

The expression for the area of the field.

Answer to Problem 32PPS

  $l^2-45l$

Explanation of Solution

Given:

The given statement is:

Width = 45 yards

Calculation:

Let length = $l$

Width = $\text{(}l-45)$

The area of the rectangle is:

  $\begin{array}{l}\text{Area of the rectangle = Length}\times width\\ =l(l-45)\\ =l^2-45l\end{array}$

(b)

To determine

The dimensions of the field.

Answer to Problem 32PPS

  $\begin{array}{l}\text{Length = 120yards}\\ \text{Width = 75yards}\end{array}$

Explanation of Solution

Given:

The given statement is:

Width = 45 yards

Calculation:

The area of the field is = 9000 square yards.

Therefore,

  $\begin{array}{l}9000=l^2-45l\\ l^2-45l-9000=0\\ (l-120)(l+75)=0\\ l=120\text{ or }l=-75\end{array}$

Hence,

  $\begin{array}{l}\text{Length}=120\text{ yards}\\ \text{Width = 120 - 45 = 75 yards}\end{array}$