Final answer:
The width of the rectangular carpet with an area of 64m², and length twice its width, is approximately 5.66 meters.
Step-by-step explanation:
To determine the width of the rectangular carpet, we need to use the information that the area of the carpet is 64m² and that the length is twice the width. Let's call the width of the carpet 'w' meters. Then, the length would be '2w' meters. The area of a rectangle is found by multiplying the length by the width, so we have:
Area = length × width
64m² = 2w × w
64m² = 2w²
Dividing both sides by 2 gives:
w² = 32
Now, taking the square root of both sides to solve for 'w':
w = √32
w = 5.66 meters (rounded to two decimal places)
Therefore, the width of the carpet is approximately 5.66 meters.