Question

2. The area of a rectangle is 8x2-32 The length of the rectangle is x- Which of the following expressions could represent the width of the rectangle?
LO
A. 8(X+2)
B. 4(X+2)
C. 4(X-2)
D. 2(X-2)

Answer 1

To find the width of the rectangle, we can use the formula for the area of a rectangle, which is:

\[ \text{Area} = \text{Length} \times \text{Width} \]

Given that the area is \( 8x^2 - 32 \) and the length is \( x \), we can express this as:

\[ 8x^2 - 32 = x \times \text{Width} \]

To find the width, we can divide the area by the length:

\[ \text{Width} = \frac{8x^2 - 32}{x} \]

Now, let's simplify \( 8x^2 - 32 \):

1. Factor out the common term from \( 8x^2 - 32 \):
\[
8x^2 - 32 = 8(x^2 - 4) = 8(x - 2)(x + 2)
\]

2. Now, substitute this back into the width expression:
\[
\text{Width} = \frac{8(x - 2)(x + 2)}{x}
\]
Simplifying this gives:
\[
\text{Width} = 8(x + 2) \cdot \frac{(x - 2)}{x}
\]

Since \( \text{Width} \) must be in a form with a simple expression, we continue by canceling out \( x \). However, let's check the options provided:

A. \( 8(x + 2) \)

B. \( 4(x + 2) \)

C. \( 4(x - 2) \)

D. \( 2(x - 2) \)

We need to compare the simplified expression \( 8 \cdot \frac{(x - 2)(x + 2)}{x} \) with the options listed.

In the options, the only expression that has a factor involving \( (x+2) \) can be split into a suitable relation that could represent the width given our found form.

The closest match here seems to be:

B. \( 4(x + 2) \)

This means that the width can be expressed with a factor that could lead to multiplication by \(x\) which leads to exact relations for setup and also produces proper geometric mean.

Therefore, the answer is:

**B. \( 4(x + 2) \)**