Final answer:
The expression for the perimeter of the triangle is 12.9x + 3y + 4z cm, found by summing the like terms of the triangle's three given side lengths.
Step-by-step explanation:
To find the perimeter of a triangle, you simply add the lengths of all three sides together. Given the side lengths are (4.5x + 7.5y) cm, (8.4x +2.5z) cm, and (1.5z - 4.5y) cm, you can combine like terms in this addition.
Perimeter = (4.5x + 7.5y) + (8.4x +2.5z) + (1.5z - 4.5y)
Combine the x terms: 4.5x + 8.4x = 12.9x
Combine the y terms: 7.5y - 4.5y = 3y
Combine the z terms: 2.5z + 1.5z = 4z
Adding these together gives the total perimeter:
Perimeter = 12.9x + 3y + 4z
Therefore, the expression representing the perimeter in centimeters of the triangle is 12.9x + 3y + 4z, which corresponds to option 3).