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

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Given:

Each side of the octagon = 5x - 6

Therefor:

Total of all 8 sides of the octagon = Perimeter = 8*(5x - 6) = 40x - 48

It is given:

Perimeter is equal to 72. Therefor:

40x - 48 = 72

==> 40x = 72 + 48 = 120

==> x = 120/40 = 3

Answer:

x = 3

The regular octagon has 8 equal sides.

Since each side measures 5x-6, its perimeter = 8 times (5x-6) = 8(5x-6). = 40x-48 which is equal to 72 as given.

Therefore the required equation is :

40x-48 = 72. We solve for x.

40x = 72+48 = 120

x = 120/40 = 3

x = 3.

Therefore each side = 5x-6 = 5*3 -6 = 9.

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**