Question

question
a triangle has side lengths of (3q + 1) centimeters, (5q - 3) centimeters, and (r - 9) centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
8q - 11 + r
-8r + 2 + 4q
-2 + 8q - 8r
-8r + 6q

Explanation:

Step1: Recall perimeter formula

Perimeter of a triangle is the sum of its three sides. So we add \((3q + 1)\), \((5q - 3)\), and \((r - 9)\).
\[
(3q + 1)+(5q - 3)+(r - 9)
\]

Step2: Combine like terms for \(q\)

Combine the \(q\)-terms: \(3q+5q = 8q\)

Step3: Combine constant terms

Combine the constant terms: \(1-3 - 9=1-(3 + 9)=1 - 12=- 11\)

Step4: Include the \(r\)-term

The \(r\)-term is just \(r\) (since there's only one \(r\)-term). So putting it all together: \(8q-11 + r\)

Answer:

\(8q - 11 + r\) (corresponding to the option " \(8q-11 + r\) ")