A polygon is regular if each of its sides has the same length. Find the perimeter of the regular polygon.

The perimeter of the polygon is __ units.

6units

Step-by-step explanation:

Since it is a regular polygon, and it has 3 equal sides it means the polygon is a quadrilateral.

From the diagram,

5 - 2x = -4x + 9 ( side of quadrilateral )

Solving for x in the equation

-2x + 4x = 9 - 5 ( collection of like terms in simple linear equation )

2x = 4

Divide through by the coefficient of x which is 2

x = 2.

Therefore, the perimeter of the polygon which equals to the total length of the polygon is

Perimeter = 2 + 2 + 2

= 6units

a) comic E will be performed first 

With no restrictions 6 comedians can perform in 6! = 720 ways

E _ _ _ _ _
we can fill the 5 blanks with the 5 letters A,B,C,D,F in 5! = 120 ways The probability of that is 120 ways out of 720 or 120/720 or 1/6.

b) comic C will perform fifth and comic B will perform last

_ _ _ _C B
 We can fill the 4 blanks with the 4 letters A,D,E,F in 4! = 24 ways. The probability of that is 24 ways out of 720 or 24/720 or 1/30

c) the comedians will perform in the following order D, E,C, A, B, F

D E C A B F
 There is just 1 way that can happen. The probability of that is 1 way out of 720 or 1/720.

d) comic A or comic B will perform first

_ _ _ A _ _
   There are 5! = 120 ways to fill those 5 blanks with the letters B,C,D,E,F.
In addition to those, there are another 5! = 120 ways to fill these 5 blanks
   _ _ _ B _  with the letters A,C,D,E,F.
That's 2(5!) = 2(120) = 240 ways. The probability of one of those is 240 ways out of 720 or 240/720 or 1/3.