Question

a triangle has side lengths of $(4m + 3n)$ centimeters, $(8m + 10p)$ centimeters, and $(2p + 2n)$ centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
$5n + 12p + 12m$
$4np + 18mp + 7mn$
$15np + 14mp$
$4p + 12m + 13n$

Explanation:

Step1: Recall perimeter formula

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. So \(P=(4m + 3n)+(8m + 10p)+(2p + 2n)\).

Step2: Remove parentheses

\(P = 4m+3n + 8m+10p+2p + 2n\).

Step3: Combine like - terms

Combine the \(m\) terms: \(4m+8m = 12m\); combine the \(n\) terms: \(3n+2n=5n\); combine the \(p\) terms: \(10p + 2p=12p\). So \(P=12m + 5n+12p\).

Answer:

A. \(5n + 12p+12m\)