Question

in the diagram below, what is the relationship between the number of rectangles and the perimeter of the figure they form? (1 point) write the function that represents the above relationship?

Explanation:

Step1: Analyze perimeter of 1 rectangle

For 1 rectangle with length $l = 5$ and width $w = 2$, the perimeter $P_1$ of a single - rectangle is given by the formula $P=2(l + w)$. So, $P_1=2(5 + 2)=2\times7 = 14$.

Step2: Analyze perimeter of 2 rectangles

When we have 2 rectangles placed side - by - side, the new length $l_2=5\times2 = 10$ and width $w_2 = 2$. The perimeter $P_2=2(10 + 2)=2\times12 = 24$.

Step3: Analyze perimeter of 3 rectangles

When we have 3 rectangles placed side - by - side, the new length $l_3=5\times3 = 15$ and width $w_3 = 2$. The perimeter $P_3=2(15 + 2)=2\times17 = 34$.

Step4: Find the function

Let $n$ be the number of rectangles. The length of the combined figure is $l_n = 5n$ and the width is $w = 2$. The perimeter $P(n)$ of the figure formed by $n$ rectangles is given by the formula $P(n)=2(5n + 2)=10n+4$.

Answer:

$P(n)=10n + 4$