Final answer:
To find the length of the shorter side of the rectangle, we can set up an equation using the given information and solve for the variable 'x'. The length of the shorter side is found to be 10 centimeters.
Step-by-step explanation:
To find the length of the shorter side of the rectangle, we can set up an equation using the given information. Let's assume one side of the rectangle is 'x'. According to the problem statement, another side is 12 centimeters shorter than twice the first side, which can be written as 2x - 12. The perimeter of a rectangle is the sum of all its sides, so we have the equation: 2x + 2(2x - 12) = 36. Simplifying this equation, we get: 6x - 24 = 36. Adding 24 to both sides, we have: 6x = 60. Finally, dividing both sides by 6, we find that x = 10. Therefore, the length of the shorter side of the rectangle is 10 centimeters.