Question
A triangle has side lengths of \( (7 m-2) \) centimeters, \( (9 m-5) \) centimeters, and \( (6 n-1) \) centimeters Which expression represents the perimeter, in centimeters, of the triangle?
Ask by Beck Higgins. in the United States
Jan 06,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The perimeter of the triangle is \( 16m + 6n - 8 \) centimeters.
Solution
To find the perimeter of the triangle, you need to sum the lengths of all its sides. Given the side lengths:
- \( 7m - 2 \) centimeters
- \( 9m - 5 \) centimeters
- \( 6n - 1 \) centimeters
**Step-by-Step Calculation:**
1. **Add the side lengths together:**
\[
(7m - 2) + (9m - 5) + (6n - 1)
\]
2. **Combine like terms:**
- Combine the terms with \( m \):
\[
7m + 9m = 16m
\]
- Combine the constants:
\[
-2 - 5 - 1 = -8
\]
- The term with \( n \) remains as is:
\[
6n
\]
3. **Write the simplified expression:**
\[
16m + 6n - 8 \text{ centimeters}
\]
**Final Answer:**
\[
16m + 6n - 8 \text{ centimeters}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To find the perimeter of the triangle, you need to add up all the side lengths. So, you would combine the expressions for the side lengths: \[ (7m - 2) + (9m - 5) + (6n - 1) \] When you simplify this, you combine like terms: \[ (7m + 9m + 6n) + (-2 - 5 - 1) = 16m + 6n - 8 \] Thus, the expression that represents the perimeter of the triangle is \( 16m + 6n - 8 \) centimeters. Another way to think about triangles is to remember that their perimeter is simply the total distance around the shape. For practical purposes, once you find this expression, you can substitute values for \( m \) and \( n \) to determine the specific perimeter for any given values.
