Question

the relationship between the perimeter and side length of a regular octagon is shown in the graph below.
what happens to the perimeter of a regular octagon as its side length increases by 1?
the perimeter increases by 16.
the perimeter increases by 4.
the perimeter increases by 1.
the perimeter increases by 8.

Explanation:

Step1: Recall octagon perimeter formula

A regular octagon has 8 equal sides. So, perimeter \( P = 8 \times \text{side length} \) (let side length be \( s \), so \( P = 8s \)).

Step2: Analyze rate of change

The slope of the perimeter - side length graph (or the coefficient in the formula) represents the change in perimeter per unit change in side length. From \( P = 8s \), when \( s \) increases by 1, \( \Delta P=8\times1 = 8 \). Alternatively, check the graph: for example, when \( s = 1 \), \( P = 8 \); when \( s = 2 \), \( P = 16 \). The change in \( P \) is \( 16 - 8 = 8 \) when \( s \) increases by 1.

Answer:

The perimeter increases by 8. (Corresponding to the option: The perimeter increases by 8)