Final answer:
After equating the expressions given for the base of the triangle and finding the value of x to be 5, all three sides of the triangle are determined. The perimeter of the triangle is found to be 34 cm by adding the lengths of all three sides. However, this answer does not match any of the provided multiple-choice answers, indicating a possible issue with the question or answer choices.
Step-by-step explanation:
To calculate the perimeter of the triangle, we first need to solve for x. We have two expressions for the sides of the triangle in terms of x: 2x for the base side, and 3x - 5 for the base side as well. Since both represent the same base side, we can equate them to find the value of x.
2x = 3x - 5
Therefore, x = 5
Now that we have the value of x, we can substitute it back into the expressions for the sides of the triangle to get their lengths:
Base side: 2x = 2(5) = 10 cm
Base side (again): 3x - 5 = 3(5) - 5 = 15 - 5 = 10 cm
Other side: 19 - x = 19 - 5 = 14 cm
Now, to find the perimeter, we add up the lengths of all three sides:
Perimeter = base side + base side + other side
Perimeter = 10 cm + 10 cm + 14 cm = 34 cm
This perimeter is not one of the answer options provided, which suggests there might be an error in the answer choices given or the question itself.