Question

1. (a.eo.2.b, 5 points) which expression can be used to represent the perimeter of the rectangle? k - 5 3(k + 5) a. 4k b. 4k+20 c. 8k d. 8k+20

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=3(k + 5)$ and $w=k - 5$.

Step2: Substitute values into formula

$P=2(3(k + 5)+(k - 5))$.
First, expand $3(k + 5)$ to get $3k+15$. So $P = 2((3k + 15)+(k - 5))$.

Step3: Simplify the expression inside parentheses

$(3k + 15)+(k - 5)=3k+15 + k-5=4k + 10$.

Step4: Multiply by 2

$P=2(4k + 10)=8k+20$.

Answer:

D. $8k + 20$