Question

a triangle has side lengths of $(5.7v - 9.8)$ centimeters, $(7.2v + 7.9)$ centimeters, and $(9.5w - 5.4)$ centimeters. which expression represents the perimeter, in centimeters, of the triangle?
answer
$\circ$ $4.1w + 11v$ $\circ$ $-1.9 + 12.9v + 4.1w$ $\circ$ $12.9v + 9.5w - 7.3$ $\circ$ $-4.1v + 15.1 + 4.1w$

Explanation:

Step1: Recall the formula for the perimeter of a triangle

The perimeter \(P\) of a triangle is the sum of the lengths of its sides. If the side lengths are \(a=(5.7v - 9.8)\), \(b=(7.2v + 7.9)\), and \(c=(9.5w-5.4)\), then \(P=a + b + c\).

Step2: Substitute the side - length expressions into the perimeter formula

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Step3: Combine like terms

For the \(v\) - terms: \(5.7v+7.2v=(5.7 + 7.2)v=12.9v\).
For the constant terms: \(-9.8+7.9-5.4=(-9.8+(7.9 - 5.4))=(-9.8 + 2.5)=-7.3\).
The \(w\) - term remains \(9.5w\).
So, \(P = 12.9v+9.5w-7.3\).

Answer:

\(12.9v + 9.5w-7.3\)