Question

A triangle has side lengths of left parenthesis, 9, m, plus, 7, n, right parenthesis(9m+7n) centimeters, left parenthesis, 7, p, plus, 10, m, right parenthesis(7p+10m) centimeters, and left parenthesis, p, minus, 4, n, right parenthesis(p−4n) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Answer 1

To find the perimeter of the triangle with given side lengths, we need to add the lengths of all three sides together.

The side lengths of the triangle are:
1. \( 9m + 7n \) cm
2. \( 7p + 10m \) cm
3. \( p - 4n \) cm

The perimeter \( P \) of the triangle can be calculated by summing these side lengths:

\[
P = (9m + 7n) + (7p + 10m) + (p - 4n)
\]

Now, let’s combine like terms:

1. For the \( m \) terms:
- \( 9m + 10m = 19m \)

2. For the \( n \) terms:
- \( 7n - 4n = 3n \)

3. For the \( p \) terms:
- \( 7p + p = 8p \)

Putting it all together, we have:

\[
P = 19m + 3n + 8p
\]

Thus, the expression representing the perimeter of the triangle, in centimeters, is:

\[
\boxed{19m + 3n + 8p}
\]