Final answer:
The lengths of the sides of the rectangle are 27 meters and 37 meters.
Step-by-step explanation:
Let's assume the length of one side of the rectangle to be x meters. Since the other side is 10 meters longer, its length will be x + 10 meters.
The formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Thus, we can write the equation as 128 = 2(x + 10) + 2x.
Simplifying the equation, we have 128 = 2x + 20 + 2x.
Combining like terms, we get 128 = 4x + 20.
Subtracting 20 from both sides, we have 4x = 108.
Dividing both sides by 4, we find that x = 27. Therefore, one side of the rectangle measures 27 meters, while the other side measures 27 + 10 = 37 meters.
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