Respuesta :

danielmaduroh

Answer:

[tex]\boxed{x=4}[/tex]

Step-by-step explanation:

From this problem, we know two things:

1. The perimeter of a regular 6-sided figure is 30 units.

2. The length of each side is x+1 units.

A regular 6-sided figure is a figure called regular hexagon, which is any polygon with exactly 6 regular sides, that is, each side measures the same length. The representation of this problem is shown below. On the other hand, the perimeter of a shape is the total length around a shape. Hence we can get a relationship between 1 and 2 as follows:

[tex]P=6(x+1) \\ \\ where \ P \ is \ the \ perimeter[/tex]

Therefore, we can calculate [tex]x[/tex]:

[tex]P=6x+6 \\ \\ 30-6=6x \\ \\ 24=6x \\ \\x=\frac{24}{6} \therefore \boxed{x=4}[/tex]

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A regular figure has all sides equal. For the given context, the value of x is given as: x = 4

What is perimeter?

Its the sum of length of the sides used to made the given figure.

What is a regular figure and its perimeter?

A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).

Suppose that length of each side of that figure be of u units, then we have the perimeter as:

[tex]P = u + u + ... + u \text{ (n times) } = n\times u[/tex] units.

For the given case, it is given that the regular figure has:

n = 6 regular sides,

u = x+1 unit (length of each sides)

Thus,

its perimeter = [tex]n \times u = 6 \times (x+1)\\[/tex]

or

[tex]30 = 6(x+1)\\\\\text{dividing both sides by 6}\\5 = (x+1)\\\\\text{Subtracting 1 from each side}\\\\4 = x\\x = 4[/tex]

Thus,

A regular figure has all sides equal. For the given context, the value of x is given as: x = 4

Learn more about perimeter here:

https://brainly.com/question/10466285

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