Question

question
the width of a rectangle measures (6p + 9) centimeters, and its length measures (3p + 6) centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
9p + 15
30p + 18
18p + 30
15p + 9
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Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \).

Step2: Substitute the given length and width

Given width \( = (6p + 9) \) cm and length \( = (3p + 6) \) cm. Substitute these into the formula:
\( P = 2\times((3p + 6) + (6p + 9)) \)

Step3: Simplify the expression inside the parentheses

First, combine like terms inside the parentheses: \( (3p + 6p) + (6 + 9) = 9p + 15 \)

Step4: Multiply by 2

Now, multiply the result by 2: \( 2\times(9p + 15) = 18p + 30 \)

Answer:

\( 18p + 30 \)