Certainly! Let's go through the problem step-by-step to find the correct equation that represents the information given.
### Step 1: Define the Width and Length
- Let the width of the rectangular swimming pool be [tex]\( x \)[/tex] meters.
- The length of the rectangular swimming pool is twice the width, so it is [tex]\( 2x \)[/tex] meters.
### Step 2: Calculate the Area
- The area of a rectangle is given by the product of its width and length.
- Therefore, the area [tex]\( A \)[/tex] of the swimming pool is:
[tex]\[
A = \text{width} \times \text{length}
\][/tex]
- Substituting the given values:
[tex]\[
A = x \times 2x
\][/tex]
### Step 3: Substitute the Given Area
- We are given that the area of the pool is 64 square meters.
- Thus, the equation becomes:
[tex]\[
x \times 2x = 64
\][/tex]
Simplifying the left side:
[tex]\[
2x^2 = 64
\][/tex]
Thus, the equation representing the information given is:
[tex]\[
2x^2 = 64
\][/tex]
Hence, the appropriate form from the given options is:
- [tex]\( x(2x) = 64 \)[/tex]
This is the correct equation that represents the scenario described for the swimming pool.
