Question

A triangle has side lengths of left parenthesis, 5, m, minus, 2, n, right parenthesis(5m−2n) centimeters, left parenthesis, 7, m, plus, 10, p, right parenthesis(7m+10p) centimeters, and left parenthesis, 8, p, minus, 9, n, right parenthesis(8p−9n) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Answer 1

To find the perimeter of the triangle with the given side lengths, we need to add the expressions representing each side:

1. The first side length is \( 5m - 2n \) centimeters.
2. The second side length is \( 7m + 10p \) centimeters.
3. The third side length is \( 8p - 9n \) centimeters.

Now, we will calculate the perimeter by summing these three side lengths:

\[ \text{Perimeter} = (5m - 2n) + (7m + 10p) + (8p - 9n) \]

Now let's combine like terms:

1. Combine \( 5m \) and \( 7m \): \[ 5m + 7m = 12m \]

2. Combine \( 10p \) and \( 8p \): \[ 10p + 8p = 18p \]

3. Combine \( -2n \) and \( -9n \): \[ -2n - 9n = -11n \]

Putting it all together, we have:

\[ \text{Perimeter} = 12m + 18p - 11n \]

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

\[ \boxed{12m + 18p - 11n} \]