Question

regular polygons have congruent sides and congruent angles. The regular octagon has a perimeter represented by the expression shown perimeter equals 48 y - 40 write an expression to represent the length of one side of the Octagon ( the octagon has 8 equal sides )

Answer 1

Since we have a regular polygon, and it has congruent sides and angles, and we have that the perimeter (the sum of all of the sides of the regular polygon) is given by:

$P=48y-40$

Then, each side of this octagon (it is a polygon with eight equal sides), is given by:

$s=\frac{P}{8}=\frac{(48y-40)}{8}\Rightarrow s=\frac{48y}{8}-\frac{40}{8}\Rightarrow s=6y-5$

Therefore, the expression to represent the length of one side of the octagon is:

$s=6y-5$

In summary, we divide the expression by 48y - 40 by 8 because each side of the octagon has the same length. Then, we divide 48y/8 = 6y, and -40/8= - 5, and the final expression is s = 6y -5 (the expression for each side of the octagon.)