Question

A triangle has side lengths of left parenthesis, 6, n, plus, 10, p, right parenthesis(6n+10p) centimeters, left parenthesis, 5, q, plus, 2, n, right parenthesis(5q+2n) centimeters, and left parenthesis, 7, q, plus, 5, p, right parenthesis(7q+5p) centimeters. Which expression represents the perimeter, in centimeters, of the triangle

Answer 1

To calculate the perimeter of the triangle, we need to sum the lengths of all three sides.

The side lengths of the triangle are given as:
1. \( 6n + 10p \)
2. \( 5q + 2n \)
3. \( 7q + 5p \)

The perimeter \( P \) of the triangle can be expressed as:

\[
P = (6n + 10p) + (5q + 2n) + (7q + 5p)
\]

Now we can combine the like terms:

1. **Terms involving \( n \):**
- \( 6n + 2n = 8n \)

2. **Terms involving \( p \):**
- \( 10p + 5p = 15p \)

3. **Terms involving \( q \):**
- \( 5q + 7q = 12q \)

Now, putting all of these together, we can express the perimeter as:

\[
P = 8n + 15p + 12q
\]

Therefore, the expression that represents the perimeter of the triangle in centimeters is:

\[
\boxed{8n + 15p + 12q}
\]