Question

a triangle has side lengths of (9a + 5b) centimeters, (8c - 6a) centimeters, and (5c + 3b) centimeters. which expression represents the perimeter, in centimeters, of the triangle? answer 13c + 8b + 3a 8bc + 14ab + 2ac 8c + 3a + 13b 8ac + 16bc submit answer

Explanation:

Step1: Recall perimeter formula

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. So \(P=(9a + 5b)+(8c - 6a)+(5c + 3b)\).

Step2: Remove parentheses

Since there are no coefficients or negative - signs outside the parentheses, the expression remains \(9a + 5b+8c - 6a+5c + 3b\).

Step3: Group like - terms

Group the \(a\) - terms, \(b\) - terms, and \(c\) - terms together: \((9a-6a)+(5b + 3b)+(8c+5c)\).

Step4: Combine like - terms

For the \(a\) - terms: \(9a-6a = 3a\); for the \(b\) - terms: \(5b + 3b=8b\); for the \(c\) - terms: \(8c+5c = 13c\). So the perimeter is \(13c + 8b+3a\).

Answer:

A. \(13c + 8b + 3a\)