Question

question 5
2 + k
4(k + 5)
part a: use the drop - down menu to choose the expression that best represents the perimeter (p) of this rectangle.
p = select
select
6k + 20
5k + 22
27k
8k + 34
10k + 44
4k + 24
54k
10k + 14
gle is 68 inches. what is the value of k?
what is the value of b?

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=4(k + 5)$ and $w=2 + k$.

Step2: Expand the length

Expand $4(k + 5)$ using the distributive property: $4(k + 5)=4k+20$.

Step3: Substitute into perimeter formula

$P = 2((4k + 20)+(2 + k))$. First simplify inside the parentheses: $(4k + 20)+(2 + k)=5k + 22$. Then $P = 2(5k + 22)$.

Step4: Distribute the 2

Using the distributive property $2(5k + 22)=10k + 44$.

Step5: Solve for k when P = 68

Set $10k + 44=68$. Subtract 44 from both sides: $10k=68 - 44$, so $10k = 24$. Divide both sides by 10: $k=\frac{24}{10}=2.4$.

Answer:

Part A: $10k + 44$
Part B: $k = 2.4$