Final answer:
The length of the longest side of the rectangle is 36 cm.
Step-by-step explanation:
Let the sides of the rectangle be 6x and 5x, where x is a common factor.
The perimeter of rectangle is given by formula 2(length + width).
So, 2(6x + 5x) = 132 cm.
Combine like terms: 2(11x) = 132 cm.
Divide both sides by 2: 11x = 66 cm.
Divide both sides by 11: x = 6 cm.
Therefore, the length of the longest side is 6x = 6(6 cm) = 36 cm.
In the context of the rectangle, the sides are determined to be 30 cm and 36 cm, considering that the length is 6 times the common factor (x) and the width is 5 times the common factor (x).