To find the width of the rectangle, we begin by understanding the relationship given between the length and the width of the rectangle. The problem states that the length of the rectangle is [tex]\(\frac{8}{3}\)[/tex] times as great as its width.
Let's denote the width of the rectangle by [tex]\(w\)[/tex]. According to the problem, the length [tex]\(l\)[/tex] can be expressed as:
[tex]\[ l = \frac{8}{3} \cdot w \][/tex]
We are also informed that the length of the rectangle is 24 feet. Therefore, we can set up the following equation:
[tex]\[ 24 = \frac{8}{3} \cdot w \][/tex]
To isolate [tex]\(w\)[/tex], we need to solve this equation for [tex]\(w\)[/tex]. First, multiply both sides of the equation by 3 to eliminate the fraction:
[tex]\[ 24 \cdot 3 = 8w \][/tex]
This simplifies to:
[tex]\[ 72 = 8w \][/tex]
Next, divide both sides of the equation by 8:
[tex]\[ \frac{72}{8} = w \][/tex]
Simplifying this, we get:
[tex]\[ w = 9 \][/tex]
So, the width of the rectangle is 9 feet.
Thus, the correct answer is:
A) 9 ft.
