Answer:
x = 3
perimeter: 18 units
Step-by-step explanation:
1. First, we should know that a regular polygon is a polygon that has all angles the same angle measure and all sides the same side length.
- For example, an equilateral triangle is a regular polygon because all angles are 60 degrees and all sides are the same length.
- This means that for the polygon in the image, 5(x+2) = 7x + 4
2. (Solving)
Step 1: Simplify both sides of the equation.
- [tex](5)(x)+(5)(2)=7x+4[/tex]
- [tex]5x + 10 = 7x + 4[/tex]
Step 2: Subtract 7x from both sides.
- [tex]5x + 10 - 7x = 7x + 4 - 7x[/tex]
- [tex]-2x + 10 = 4[/tex]
Step 3: Subtract 10 from both sides.
- [tex]-2x + 10 - 10 = 4 - 10[/tex]
- [tex]-2x = -6[/tex]
Step 4: Divide both sides by -2.
- [tex]\frac{-2x}{-2} = \frac{-6}{-2}[/tex]
- [tex]x = 3[/tex]
Step 5: Check if solution is correct.
- [tex]5(3+2)=7(3)+4[/tex]
- [tex]5(5)=21+4[/tex]
- [tex]25 = 25[/tex]
3. Now, since this polygon has 6 sides, it's a hexagon. To find the perimeter of a hexagon, we just multiply the length of one side 6 times.
- [tex]3(6)[/tex]
- [tex]18[/tex]
Therefore, x = 3 and the perimeter is 18 units.
