Final answer:
The width of the rectangle is 39 meters and the length is 78 meters.
Step-by-step explanation:
To find the dimensions of the rectangle, let the width be x meters.
The length of the rectangle is twice its width, so the length is 2x meters. The formula for the perimeter of a rectangle is P = 2(length + width).
Substituting the given perimeter of 234 meters into the equation: 234 = 2(2x + x).
Simplifying the equation: 234 = 2(3x). Dividing both sides by 2: 117 = 3x.
Lastly, dividing both sides by 3: 39 = x. Therefore, the width of the rectangle is 39 meters and the length is twice the width, so the length is 2 * 39 = 78 meters.