A triangle has side lengths of left bracket, 5, n, plus, 3, p, right bracket(5n+3p) centimeters, left bracket, 9, n, plus, 8, q, right bracket(9n+8q) centimeters, and left bracket, 6, q, plus, 9, p, right bracket(6q+9p) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?
15, q, plus, 14, n, plus, 11, p15q+14n+11p
20, p, q, plus, 20, n, q20pq+20nq
12, p, plus, 14, q, plus, 14, n12p+14q+14n
17, n, q, plus, 8, n, p, plus, 15, p, q17nq+8np+15pq
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