Chapter 11.3, Problem 2STP

For Exercises 1-4, choose the correct letter.

If the area of a rectangle is $x^2-9$, can the length be $x-1$?

1. Yes; it divides perfectly.
2. No; the length would be larger,
3. Yes; but the width will have a remainder.
4. No; the measurements of the rectangle must multiply and divide evenly.

To determine

To explain whether the statement is correct or not

Answer to Problem 2STP

The correct answer is (I)

Explanation of Solution

Given information:

If the area of a rectangle is $\left(x^2-9\right)$ , can the length be $\left(x-1\right)$

The statement is explain as

  $\begin{array}{l}\text{Area of rectangle}=\text{length}\times \text{breadth}\\ \text{breadth}=\frac{\text{Area of rectangle}}{\text{length}}\end{array}$

The area is $\left(x^2-9\right)$ and the length is $\left(x-1\right)$

Since,

  $\left(x^2-9\right)$ is not perfectly divisible by $\left(x-1\right)$

Thus the length cannot be $\left(x-1\right)$ for that rectangle

Hence,

The correct answer is (I)