Question

question
a triangle has side lengths of $(4f + 2)$ centimeters, $(7f + 7)$ centimeters, and $(g + 2)$ centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
$6f + 14 + 3g$
$3g + 20f$
$11f + 9 + 3g$
$g + 11f + 11$
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Explanation:

Step1: Recall the formula for the perimeter of a triangle

The perimeter \(P\) of a triangle with side lengths \(a\), \(b\), and \(c\) is \(P=a + b + c\). Here, \(a=(4f + 2)\), \(b=(7f + 7)\), and \(c=(g + 2)\). So, \(P=(4f + 2)+(7f + 7)+(g + 2)\).

Step2: Remove the parentheses

Using the associative property of addition, \(P = 4f+2 + 7f+7+g + 2\).

Step3: Combine like - terms

Combine the \(f\) - terms: \(4f+7f=(4 + 7)f=11f\). Combine the constant terms: \(2 + 7+2=11\). The \(g\) - term remains as it is. So, \(P=g + 11f+11\).

Answer:

\(g + 11f+11\)