Question

the width of a rectangle measures $(5v - 2w)$ centimeters, and its length measures $(6v + 7w)$ centimeters. which expression represents the perimeter, in centimeters, of the rectangle? answer $10w + 22v$ $22v + 10$ $-2 + 14w + 22v$ $11v + 5$ submit answer

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

The formula for the perimeter \(P\) of a rectangle is \(P = 2(l + w)\), where \(l\) is the length and \(w\) is the width.
Given \(l=(6v + 7w)\) and \(w=(5v - 2w)\).

Step2: Substitute the length and width into the formula

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Step3: Combine like - terms inside the parentheses

Combine the \(v\) - terms (\(6v+5v = 11v\)) and the \(w\) - terms (\(7w-2w = 5w\)). So, \(P = 2(11v + 5w)\).

Step4: Distribute the 2

Using the distributive property \(a(b + c)=ab+ac\) (here \(a = 2\), \(b = 11v\), \(c = 5w\)), we get \(P=2\times11v+2\times5w=22v + 10w\).

Answer:

\(10w + 22v\)