Each side of a regular octagon is represented by 5x6 What i

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

Solution

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