Question

part a: use the drop - down menu to choose the expression that best represents the perimeter (p) of this rectangle.
p = select
part b: the perimeter of the rectangle is 68 inches. what is the value of k?
k = select
question 6
what is the value of b?
7 - 5b = - 8(2b - 5)

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P=2l + 2w$, where $l$ is the length and $w$ is the width. Here, $l = 4(k + 5)$ and $w=2 + k$. So $P = 2(2 + k)+2\times4(k + 5)$.

Step2: Simplify perimeter expression for Part A

\[

$$\begin{align*} P&=2(2 + k)+8(k + 5)\\ &=4+2k+8k + 40\\ &=10k + 44 \end{align*}$$

\]

Step3: Solve for $k$ in Part B

Set $P = 68$. So $10k+44 = 68$. Subtract 44 from both sides: $10k=68 - 44=24$. Then divide both sides by 10: $k=\frac{24}{10}= 4$.

Answer:

Part A: $P = 2(2 + k)+2\times4(k + 5)$
Part B: $k = 4$