Final answer:
The shortest side is 25 cm, the longest side is 50 cm, and the third side is 40 cm.
Step-by-step explanation:
Let's denote the length of the shortest side as x.
The longest side is twice as long as the shortest side, so it is 2x.
The third side is 10 cm shorter than the longest side, so it is 2x - 10.
Since the perimeter is the sum of the lengths of all three sides, we can write the equation: x + 2x + (2x - 10) = 115
Simplifying the equation, we get 5x - 10 = 115
Adding 10 to both sides, we get 5x = 125
Dividing both sides by 5, we get x = 25
Therefore, the shortest side is 25 cm, the longest side is 2x = 50 cm, and the third side is 2x - 10 = 40 cm.