Question

A triangle has side lengths of left parenthesis, 6, v, plus, 3, right parenthesis(6v+3) centimeters, left parenthesis, 2, v, plus, 5, right parenthesis(2v+5) centimeters, and left parenthesis, 8, w, plus, 5, right parenthesis(8w+5) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Answer 1

To find the perimeter of the triangle, we need to add the lengths of all three sides together.

The side lengths are given as:

1. \( 6v + 3 \) cm
2. \( 2v + 5 \) cm
3. \( 8w + 5 \) cm

The perimeter \( P \) of the triangle can be calculated by summing these expressions as follows:

\[
P = (6v + 3) + (2v + 5) + (8w + 5)
\]

Now, let’s combine the expressions:

1. Combine the terms involving \( v \):
\[
6v + 2v = 8v
\]

2. Combine the constant terms:
\[
3 + 5 + 5 = 13
\]

Thus, the perimeter can be expressed as:

\[
P = 8v + 8w + 13
\]

So, the expression that represents the perimeter of the triangle in centimeters is:

\[
\boxed{8v + 8w + 13}
\]