A triangle has side lengths of \( (7 m-2) \) centimeters, \( (9 m-5) \) centimeters, and ( \( 6 n- \) centimeters. Which expression represents the perimeter, in centimeters, of the triangle? Answer

The expression that represents the perimeter of the triangle is obtained by adding the lengths of all three sides together. Therefore, the perimeter \( P \) can be expressed as: \[ P = (7m - 2) + (9m - 5) + (6n) \] Simplifying this gives: \[ P = 16m + 6n - 7 \text{ centimeters.} \] So, the total perimeter of the triangle is \( 16m + 6n - 7 \) centimeters. To fully visualize how perimeter plays a vital role, remember that it's the total distance around a shape, a crucial tool in surveying, architecture, and even landscaping! Perimeter calculations ensure proper material measurements for creation and design. While calculating the perimeter, watch out for common mistakes such as misplacing parentheses or forgetting to account for every term involved in the addition. Sometimes, students lift the wrong constants or variables, leading to incorrect totals—so double-check your work!