Question

this question is worth 3 credits. the figure below shows the dimensions of a rug shaped like a rectangle. image of a rectangle with length 9 feet and width 2x feet the area of the rug is 54 square feet. write and solve an equation to determine the value of x. be sure to use the unknown, x, in your equation. show your work. answer x = ______

Explanation:

Step1: Recall area formula for rectangle

The area \( A \) of a rectangle is given by the formula \( A = \text{length} \times \text{width} \). For this rug, the length is \( 9 \) feet and the width is \( 2x \) feet, and the area is \( 54 \) square feet. So we can write the equation: \( 9\times(2x)=54 \).

Step2: Simplify the left - hand side

Simplify \( 9\times(2x) \) to get \( 18x \). So our equation becomes \( 18x = 54 \).

Step3: Solve for \( x \)

To solve for \( x \), we divide both sides of the equation \( 18x = 54 \) by \( 18 \). That is, \( x=\frac{54}{18} \).

Step4: Calculate the value of \( x \)

\( \frac{54}{18}=3 \).

Answer:

\( x = 3 \)