Question

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

Explanation:

Step1: Identify length and width variables

Let the number of rectangles be $x$ and the perimeter be $y$. For 1 rectangle, length $l = 5$, width $w=3$. The perimeter of 1 rectangle $P_1=2(5 + 3)=16$.

Step2: Analyze change with more rectangles

When we have $x$ rectangles placed side - by - side, the length of the combined figure is $5x$ and the width remains $3$. The perimeter formula for a rectangle is $y = 2(5x+3)$.

Step3: Simplify the formula

Expand $y = 2(5x + 3)$ using the distributive property: $y=10x + 6$.

Answer:

$y = 10x+6$