Each side of a regular octagon is represented by 5x-6 . What is x if the perimeter is 72.

First, we'll have to establish the fact that a regular
octagon has 8 equal sides.

We'll note as P the perimeter
and s each side of the octagon.

We'll calculat ethe
perimeter of the octagon:

P = s1 + s2 + ... +
s8 

But s1 = s2= ... = s8  =5x -
6

P = 8(5x-6)

From
enunciation, we'll have P = 72 and we'll substitute it into the above
relation:

72 = 8(5x-6)

We'll
remove the brackets:

72 = 40x -
48

We'll subtract 72 both sides and we'll use symmetric
property:

40x - 120 = 0

We'll
subtract 120 both sides:

40x =
120

We'll divide by
40:

x =
3

So, each side of the regular octagon will
measure:

s = 5x - 6

s = 5*3 -
6

s = 15-6

s =
9