Question

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a triangle has side lengths of (6v + 3) centimeters, (2v + 5) centimeters, and (8w + 5) centimeters. which expression represents the perimeter, in centimeters, of the triangle? answer 9v + 7 + 13w 8w + 8v + 13 8v + 8 + 13w 16v + 13w

Explanation:

Step1: Recall perimeter formula

Perimeter of a triangle is the sum of its three sides. So we add \((6v + 3)\), \((2v + 5)\), and \((8w + 5)\).
\[
(6v + 3)+(2v + 5)+(8w + 5)
\]

Step2: Combine like terms for \(v\)

Combine the terms with \(v\): \(6v+2v = 8v\).

Step3: Combine constant terms

Combine the constant terms: \(3 + 5+5=13\).

Step4: Combine with \(w\) term

The term with \(w\) is \(8w\). So the perimeter is \(8w + 8v+13\).

Answer:

\(8w + 8v + 13\) (corresponding to the option "8w + 8v + 13")