Answer:
The value of N is 4
Step-by-step explanation:
∵ The perimeter of any figure is the sum of its sides
∵ The sides of an irregular pentagon are (x+8), (x+6), (x+4), (x+2), x
∴ Its perimeter = x + 8 + x + 6 + x + 4 + x + 2 + x
→ Add the like terms
∴ Its perimeter = 5x + 20 ⇒ (1)
∵ The formula for the perimeter of an irregular pentagon is 5(x + N)
∴ The formula of the perimeter = 5(x + N) = 5(x) + 5(N)
∴ The formula of the perimeter = 5x + 5N ⇒ (2)
→ Equate (1) and (2)
∴ 5x + 20 = 5x + 5N
→ Subtract 5x from both sides
∵ 5x - 5x + 20 = 5x - 5x + 5N
∴ 20 = 5N
→ Divide both sides by 5
∴ [tex]\frac{20}{5}=\frac{5N}{5}[/tex]
∴ 4 = N
∴ The value of N is 4
