The problem states that four times the perimeter of a regular pentagon plus 12 cm equals 132 cm. We are asked to find the length of one side of the pentagon, given that the perimeter of a pentagon is $5x$, where $x$ is the length of one side.

1. Problem Description

The problem states that four times the perimeter of a regular pentagon plus 12 cm equals 132 cm. We are asked to find the length of one side of the pentagon, given that the perimeter of a pentagon is $5x$, where $x$ is the length of one side.

2. Solution Steps

Let $x$ be the length of one side of the regular pentagon.

The perimeter of the pentagon is $5x$.

Four times the perimeter of the pentagon is $4(5x) = 20x$.

The problem states that four times the perimeter plus 12 cm is 132 cm. So we have the equation:

$20x + 12 = 132$

Subtract 12 from both sides of the equation:

$20x = 132 - 12$

$20x = 120$

Divide both sides by 20:

$x = \frac{120}{20}$

$x = 6$

Therefore, the length of one side of the pentagon is 6 cm.

3. Final Answer

6 cm