Question

a triangle has side lengths of $(7r - 10)$ centimeters, $(5r + 5)$ centimeters, and $(s + 8)$ centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
$\square$ $3 + s + 12r$ $\bigcirc$ $7r + 9s$
$\square$ $-5 + 12r + 9s$ $\bigcirc$ $9s + 10 - 3r$

Explanation:

Step1: Recall perimeter formula

Perimeter of a triangle is the sum of its three sides. So, we need to add \((7r - 10)\), \((5r + 5)\), and \((s + 8)\).
\[
(7r - 10)+(5r + 5)+(s + 8)
\]

Step2: Combine like terms for \(r\)

Combine the terms with \(r\): \(7r+5r = 12r\)

Step3: Combine constant terms

Combine the constant terms: \(- 10 + 5+8=-10 + 13 = 3\)

Step4: Write the final expression

After combining, we get \(12r+s + 3\) or \(3 + s+12r\)

Answer:

\(3 + s + 12r\) (the first option)