Question

a triangle has side lengths of (5k − 3) centimeters, (k + 1) centimeters, and (m − 7) centimeters. which expression represents the perimeter, in centimeters, of the triangle?

answer
○ −6m + 4k
○ 6k − 6m − 2
○ −6m + 2k + 2
○ m − 9 + 6k
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Explanation:

Step1: Recall perimeter formula

Perimeter of a triangle is the sum of its three sides. So, we add the three side lengths: \((5k - 3)+(k + 1)+(m - 7)\).

Step2: Combine like terms

First, combine the \(k\)-terms: \(5k + k=6k\).
Then, combine the constant terms and the \(m\)-term: \(-3 + 1-7+m=-9 + m\).
So, the perimeter is \(6k+m - 9\), which can be rewritten as \(m - 9+6k\).

Answer:

\(m - 9 + 6k\) (the option with this expression)