SOLUTION: A polygon is regular if each of its sides has the same length. Find the perimeter of these regular polygons. a. Triangle with sides equaling: side 1= 5-2x side 2= -4x+9 base i

Algebra ->  Polygons -> SOLUTION: A polygon is regular if each of its sides has the same length. Find the perimeter of these regular polygons. a. Triangle with sides equaling: side 1= 5-2x side 2= -4x+9 base i      Log On


   

Question 1048305: A polygon is regular if each of its sides has the same length. Find the perimeter of these regular polygons.
a.
Triangle with sides equaling:
side 1= 5-2x
side 2= -4x+9
base is blank
b. 5 sided Polygon
side 1= 3(x-1)
3 other sides are blank
base= 5x-6
Answer by KMST(5397) About Me  (Show Source):
You can put this solution on YOUR website!
"Find the perimeter of these regular polygons" tells you that they are regular polygons, meaning that (for a and b) each of its sides has the same length
a.
Triangle with sides equaling:
side 1= 5-2x
side 2= -4x+9
Since the three sides have the same length that length is
5-2x=-4x%2B9 .
So we solve for x, and then find 5-2x , the length of each side.
5-2x=-4x%2B9
5-2x%2B4x-5=-4x%2B9%2B4x-5
4x-2x=9-5
2x=4
x=4%2F2
x=2
5-2x=5-2%2A2
5-2x=5-4
5-2x=1 is the length of each one of the three sides of this regular triangle (an equilateral triangle).
So the perimeter is 3%2A1=highlight%283%29 .
b.
5 sided Polygon
side 1= 3(x-1)
3 other sides are blank
base= 5x-6
Since it is a regular polygon the length is the same for all sides.
It is 5x-6=3%28x-1%29 .
Once again, we solve for x , and then use x to find the length of each side.
5x-6=3%28x-1%29
5x-6=3x-3
5x-6-3x%2B6=3x-3-3x%2B6
5x-3x=-3%2B6
2x=3
x=3%2F2
So, the length of each side is
3%283%2F2-1%29=3%281%2F2%29=3%2F2 or 5%283%2F2%29-6=15%2F2-12%2F2=3%2F2 .
With 5 sides, each measuring 3%2F2 ,
the perimeter of that 5 sided regular polygon (a regular pentagon) is
5%2A%283%2F2%29=highlight%2815%2F2=7%261%2F2%29