Final answer:
The lengths of the sides of the triangle are 24 centimeters, 24 centimeters, and 32 centimeters.
Step-by-step explanation:
To find the lengths of the sides of the triangle, let's first identify the information given. We know that the perimeter of the triangle is 80 centimeters. We also know that two sides are equally long, so let's represent their length as 'x'. The third side is 8 centimeters longer than the others, so its length can be represented as 'x + 8'.
The perimeter of a triangle is the sum of the lengths of its sides. Therefore, we can write the equation: x + x + (x + 8) = 80. Combining like terms, we get 3x + 8 = 80.
To solve for 'x', we subtract 8 from both sides of the equation: 3x = 72. Dividing both sides by 3, we find that x = 24.
So the lengths of the three sides of the triangle are: x = 24 centimeters, x = 24 centimeters, and x + 8 = 32 centimeters.