Question

type the correct answer in the box. use numerals instead of words.
if the perimeter of this triangle is 15 centimeters, what is the value of n?
triangle with sides labeled n, 5n - 6, 2n + 1
express your answer as a decimal number.
n = box

Explanation:

Step1: Recall perimeter formula

The perimeter of a triangle is the sum of its three sides. So, we add the three side lengths: \( n + (2n + 1) + (5n - 6) \).

Step2: Set up the equation

Since the perimeter is 15, we have the equation: \( n + 2n + 1 + 5n - 6 = 15 \).

Step3: Combine like terms

Combine the \( n \)-terms and the constant terms: \( (n + 2n + 5n) + (1 - 6) = 15 \), which simplifies to \( 8n - 5 = 15 \).

Step4: Solve for \( n \)

Add 5 to both sides: \( 8n - 5 + 5 = 15 + 5 \), so \( 8n = 20 \). Then divide both sides by 8: \( n = \frac{20}{8} = 2.5 \).

Answer:

2.5