Question

a triangle has side lengths of $(q + r)$ centimeters, $(5q - 10s)$ centimeters, and $(5s - 7r)$ centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
$-16rs + 11qs$ $-2rs + 2qr - 5qs$
$6q - 6r - 5s$ $6q - 2s - 9r$

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle is the sum of the lengths of its sides. So $P=(q + r)+(5q - 10s)+(5s - 7r)$.

Step2: Remove parentheses

$P = q + r+5q - 10s+5s - 7r$.

Step3: Combine like - terms

Combine the $q$ terms: $q + 5q=6q$. Combine the $r$ terms: $r-7r=-6r$. Combine the $s$ terms: $-10s + 5s=-5s$. So $P = 6q-6r - 5s$.

Answer:

$6q - 6r - 5s$