Question

A triangle has side lengths of left parenthesis, 5, k, minus, 3, right parenthesis(5k−3) centimeters, left parenthesis, k, plus, 1, right parenthesis(k+1) centimeters, and left parenthesis, m, minus, 7, right parenthesis(m−7) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Answer 1

To find the perimeter of a triangle, you simply add the lengths of its sides together.

Given the side lengths are:
1. \(5k - 3\) cm
2. \(k + 1\) cm
3. \(m - 7\) cm

The expression for the perimeter \(P\) of the triangle is:

\[
P = (5k - 3) + (k + 1) + (m - 7)
\]

Now, to simplify this expression, we can combine like terms:

1. Combine the terms involving \(k\):
- \(5k + k = 6k\)

2. Combine the constant terms:
- \(-3 + 1 - 7 = -9\)

Putting it all together, we have:

\[
P = 6k - 9 + m
\]

Thus, the expression that represents the perimeter of the triangle is:

\[
P = 6k + m - 9
\]