Question

model with mathematics the regular octagon has a perimeter represented by the expression shown. write an expression to represent the length of one side of the octagon. perimeter = 48y - 40

Explanation:

Step1: Recall perimeter of regular octagon

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

Step2: Solve for side length

Given \( P = 48y - 40 \), and \( P = 8s \), we solve for \( s \) by dividing both sides by 8.
\( s=\frac{48y - 40}{8} \)
Simplify the expression: \( \frac{48y}{8}-\frac{40}{8}=6y - 5 \)

Answer:

\( 6y - 5 \)