Final answer:
The perimeter of the triangle is found by summing the lengths of all sides. After all expressions are summed and like terms combined, the correct expression for the perimeter is 7.8w + 19.8y + 1.2x, which does not match any of the given options.
Step-by-step explanation:
To calculate the perimeter of the triangle with side lengths given by the expressions (2.6w-4.2x), (1.3w+8.1y), and (3.6y+9.6x), we simply need to add these side lengths together.
The first side is (2.6w-4.2x), and since it is mentioned twice, its total contribution will be 2 times whatever the expression is, which is 2(2.6w-4.2x) = 5.2w - 8.4x. The second side (1.3w+8.1y) also appears twice, so its contribution is 2(1.3w+8.1y) = 2.6w + 16.2y. Lastly, the third side (3.6y+9.6x) does not need to be multiplied since it is mentioned only once.
The perimeter (P) can be expressed by the sum of these contributions: P = (5.2w - 8.4x) + (2.6w + 16.2y) + (3.6y+9.6x). After combining like terms, the expression simplifies to P = 7.8w + 19.8y + 1.2x. None of the options provided in the question exactly match this result, so it appears there is an issue with the options given. It's important to carefully recheck the question and the solution.