Question

A formula for the perimeter of an irregular pentagon is 5(x+N) where N is a number the sides are (x+8)(x+6)(x+4)(x+2)(x) work out value of N

Answer 1

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

∴ $\frac{20}{5}=\frac{5N}{5}$

∴ 4 = N

∴ The value of N is 4