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To find the perimeter of the triangle, we need to sum the lengths of all its sides. The given side lengths are in terms of n, p, and q as follows:
1st side: (5n + 3p) cm
2nd side: (9n + 8q) cm
3rd side: (6q + 9p) cm
The perimeter (P) is the sum of these lengths:
P = (5n + 3p) + (9n + 8q) + (6q + 9p)
To calculate this, we combine like terms:
P = 5n + 3p + 9n + 8q + 6q + 9p
P = (5n + 9n) + (3p + 9p) + (8q + 6q)
P = 14n + 12p + 14q
The correct expression representing the perimeter of the triangle, in centimeters, is:
12p + 14q + 14n