Question

question
the width of a rectangle measures (7.6v + 2.6) centimeters, and its length measures (3.5v − 4.4) centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
○ −1.8 + 20.4v ○ 22.2v − 3.6
○ 10.2v − 0.9 ○ 11.1v − 1.8
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Explanation:

Step1: Recall the perimeter formula

The perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width.

Step2: Substitute the given expressions

Given \(w=(7.6v + 2.6)\) and \(l=(3.5v-4.4)\), then \(P = 2[(7.6v + 2.6)+(3.5v - 4.4)]\).

Step3: Simplify inside the brackets

\((7.6v+2.6)+(3.5v - 4.4)=7.6v+3.5v+2.6 - 4.4=(7.6 + 3.5)v+(2.6-4.4)=11.1v-1.8\).

Step4: Multiply by 2

\(P = 2(11.1v-1.8)=2\times11.1v-2\times1.8 = 22.2v-3.6\).

Answer:

\(22.2v - 3.6\)