Final answer:
The perimeter of the triangle, given by the expressions (46 - 5c), (96 + 10d), and (6d - 8c) centimeters, simplifies to 142 - 13c + 16d centimeters. Without specific values for 'c' and 'd', a numerical value for the perimeter cannot be determined.
Step-by-step explanation:
To find the perimeter of the triangle, we need to add the lengths of all the sides together. The side lengths of the triangle are given as (46 - 5c) centimeters, (96 + 10d) centimeters, and (6d - 8c) centimeters. Perimeter = (46 - 5c) + (96 + 10d) + (6d - 8c). To add these expressions, we should combine them like terms. Since there are no given values for 'c' and 'd', we can only simplify the expression as follows: Perimeter = (46 + 96) + (-5c - 8c) + (10d + 6d). Perimeter = 142 + (-13c) + (16d). Without the specific values for 'c' and 'd', we cannot calculate a numerical value for the perimeter. So, we conclude the perimeter in terms of 'c' and 'd' is 142 - 13c + 16d centimeters.