Question

find the perimeter. simplify your answer.

Explanation:

Step1: Recall the formula for the perimeter of a triangle

The perimeter \(P\) of a triangle is \(P=a + b+ c\), where \(a\), \(b\), and \(c\) are the side - lengths of the triangle. Here, \(a = 7c\), \(b=6c - 5\), and \(c = 4c+4\).

Step2: Substitute the side - lengths into the perimeter formula

\(P=7c+(6c - 5)+(4c + 4)\)

Step3: Remove the parentheses

\(P=7c+6c-5 + 4c+4\)

Step4: Combine like terms

Combine the \(c\) terms: \(7c+6c + 4c=(7 + 6+4)c=17c\). Combine the constant terms: \(-5 + 4=-1\)

Answer:

\(17c-1\)