Question

Each side of a regular polygon is 2.5cm in length. The perimeter of the polygon is 12.5cm. How many sides does the polygon have?​

Answer 1

Answer :

›»› The polygon has 5 sides

Given :

• Length of regular polygon = 2.5 cm
• Perimeter it regular polygon = 12.5 cm

To Find :

• How many sides does the polygon have?

How to Find?

❒ Here in this question we have to find How many sides does the polygon have. So, firstly we have to assume that the Number of sides as a variable.

And We know that the perimeter is equal to the sum of all sides, in regular polygon, all sides are same so,

Perimeter = Number of sides * Length of sides.

Now we'll easily find the Number of sides.

Let's find Number of sides...

Required Solution :

Let ,

The Number of sides be "x"

→ Perimeter = Number of sides * Length of sides

$\tt{: \implies 12.5 = x \times 2.5}$

$\tt{: \implies x = \dfrac{12.5}{2.5} }$

$\tt{: \implies x = \dfrac{ \frac{125}{10} }{ \frac{25}{10} } }$

$\tt{: \implies x = \dfrac{125}{10} \div \dfrac{25}{10} }$

$\tt{: \implies x = \dfrac{125}{ \cancel{10}} \times \dfrac{ \cancel{10}}{25} }$

$\tt{: \implies x = \dfrac{ \cancel{125}}{ \cancel{25}} }$

$\tt{: \implies x = \cancel{\dfrac{25}{5} }}$

$\frak{: \implies \underline{\boxed{\pink{ \frak{x = 5} }}}}$

║Hence, the polygon has 5 sides.║

Answer 2

Given :-

• Each side of a regular polygon is 2.5 cm in length. The perimeter of the polygon is 12.5 cm

To Find :-

• How many sides does the polygon have ?

Solution :-

Let,

• The Number of sides be “n”

We have,

• Length of the polygon = 2.5 cm
• Perimeter of the polygon = 12.5 cm

We know that,

➳ Perimeter of the polygon = Number of sides × Length of sides

Where,

• Perimeter of the polygon = 12.5 cm
• Number of sides = n
• Length of sides = 2.5 cm

Substituting the values we get,

➠ 12.5 = n × 2.5

➠ n = (2.5)/(12.5)

➠ n = 125/10/25/10

➠ n = (125/10) ÷ (25/10)

➠ n = 125/25

➠ n = 5

Thus, the polygon has 5 sides$</strong><strong>.</strong><strong>$