Question

the width of a rectangle measures $(9v - 5w)$ centimeters, and its length measures $(9v + 6w)$ centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
$1 + 18v$
$2 + 36v$
$36v + 2w$
$-5 + 12w + 36v$
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Explanation:

Step1: Recall the formula for the perimeter of a rectangle

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

Step2: Substitute the given expressions for length and width

Here, \(l=(9v + 6w)\) and \(w=(9v - 5w)\). So, \(P=2[(9v + 6w)+(9v - 5w)]\).

Step3: Simplify the expression inside the brackets

$$
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$$

Step4: Multiply by 2

\(P = 2(18v + w)=36v+2w\)

Answer:

\(36v + 2w\)