Question

the width of a rectangle measures $(9p + 7)$ centimeters, and its length measures $(p + 10)$ centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
$10p + 17$ $22 + 32p$
$16p + 11$ $20p + 34$

Explanation:

Step1: Recall perimeter formula for rectangle

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

Step2: Substitute length and width

Given width \( = 9p + 7 \) and length \( = p + 10 \), substitute into the formula:
\( P = 2\times((p + 10) + (9p + 7)) \)

Step3: Simplify inside the parentheses

Combine like terms inside the parentheses: \( (p + 10) + (9p + 7) = p + 9p + 10 + 7 = 10p + 17 \)

Step4: Multiply by 2

Multiply the result by 2: \( P = 2\times(10p + 17) = 20p + 34 \)

Answer:

\( 20p + 34 \) (corresponding to the option with this expression)