Question

a triangle has side lengths of (5m - 2n) centimeters, (7m + 10p) centimeters, and (8p - 9n) centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
18p + 12m - 11n
6n + 12m + p
-np + 17mp + 3mn
20mp - np

Explanation:

Step1: Recall perimeter formula

Perimeter of a triangle is the sum of its three sides. So, we add the three given side lengths: \((5m - 2n)+(7m + 10p)+(8p - 9n)\).

Step2: Combine like terms for \(m\)

For the \(m\) terms: \(5m + 7m = 12m\).

Step3: Combine like terms for \(n\)

For the \(n\) terms: \(-2n- 9n=-11n\).

Step4: Combine like terms for \(p\)

For the \(p\) terms: \(10p + 8p = 18p\).

Step5: Combine all terms

Putting it all together, we get \(12m-11n + 18p\) or \(18p + 12m-11n\).

Answer:

\(18p + 12m - 11n\) (the first option among the given choices)