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; 4mp + 18mp + 7mn; 15mp + 14mp; 4p + 12m + 12n

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

For the $m$ terms: $4m+8m = 12m$. For the $n$ terms: $3n+2n=5n$. For the $p$ terms: $10p + 2p=12p$. So $P=12m + 5n+12p$.

Answer:

$5n + 12p+12m$