Question

a triangle has side lengths of (4m + 3n) centimeters, (8m + 10p) centimeters, and (2p + 2n) centimeters. which expression represents the perimeter, in centimeters, of the triangle?

answer
○ ( 5n + 12p + 12m )
○ ( 15np + 14mp )
○ ( 4np + 18mp + 7mn )
○ ( 4p + 12m + 13n )
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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 given side lengths: \((4m + 3n)+(8m + 10p)+(2p + 2n)\).

Step2: Combine like terms

First, combine the \(m\)-terms: \(4m + 8m = 12m\).
Then, combine the \(n\)-terms: \(3n + 2n = 5n\).
Next, combine the \(p\)-terms: \(10p + 2p = 12p\).

Step3: Form the perimeter expression

Putting the combined terms together, the perimeter is \(12m + 5n + 12p\) (or \(5n + 12p + 12m\) when reordered).

Answer:

\(5n + 12p + 12m\) (corresponding to the first option among the choices)