Question

A triangle has side lengths of left parenthesis, 9, v, minus, 7, w, right parenthesis(9v−7w) centimeters, left parenthesis, 7, v, plus, 10, x, right parenthesis(7v+10x) centimeters, and left parenthesis, 8, x, plus, 5, w, right parenthesis(8x+5w) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Answer 1

To find the perimeter of the triangle with the given side lengths, we need to sum the expressions for each side.

The side lengths are:
1. \( 9v - 7w \) centimeters
2. \( 7v + 10x \) centimeters
3. \( 8x + 5w \) centimeters

The perimeter \( P \) of the triangle can be expressed as the sum of these side lengths:

\[
P = (9v - 7w) + (7v + 10x) + (8x + 5w)
\]

Now, let's combine like terms:

1. **Combine terms with \( v \)**:
- \( 9v + 7v = 16v \)

2. **Combine terms with \( x \)**:
- \( 10x + 8x = 18x \)

3. **Combine terms with \( w \)**:
- \( -7w + 5w = -2w \)

Putting it all together, the expression for the perimeter of the triangle is:

\[
P = 16v + 18x - 2w
\]

Thus, the expression that represents the perimeter of the triangle in centimeters is

\[
\boxed{16v + 18x - 2w}
\]