Question

the width of a rectangle measures $(3b + 5)$ centimeters, and its length measures $(8b + 6)$ centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
$\bigcirc$ $8b + 14$ $\bigcirc$ $16b + 28$
$\bigcirc$ $22 + 22b$ $\bigcirc$ $11 + 11b$

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

The length is \( (8b + 6) \) and the width is \( (3b + 5) \). So we first find the sum of length and width: \( (8b + 6)+(3b + 5) \).
Combine like terms: \( 8b+3b + 6 + 5=11b + 11 \).

Step3: Multiply by 2 to get the perimeter

Now multiply this sum by 2: \( 2\times(11b + 11) \).
Using the distributive property \( 2\times11b+2\times11 = 22b+22=22 + 22b \).

Answer:

\( 22 + 22b \) (corresponding to the option "22 + 22b")