Question

10. The perimeter of a regular pentagon is 100 cm. How long is its each side? 1. A piece of string is 30 cm long. What will be the length of each side if the string is used to form:​

Answer 1

Answer:

If all the sides of a pentagon are of equal length, it is known as a regular pentagon. In this case, the perimeter of the pentagon can be calculated with the help of the formula, Perimeter = 5 × side length. For example, if one side of a regular pentagon is 8 units, its perimeter will be, P = 5 × 8 = 40 units.

Answer 2

Q - The perimeter of a regular pentagon is 100 cm. How long is its each side?

Solution :-

A regular pentagon has five sides o equal measures.

Perimeter of regular pentagon = 100 cm

Each side =?

The perimeter of regular pentagon = 5 × side

⇒ 5 × side = 100 cm

⇒ side = 100 / 5 = 20 cm

Therefore, each side of the regular pentagon is 20 cm.

Q- A piece of string is 30cm long. What will be the length of each side if the string is used to form-

A. a square?

B. an equilateral triangle?

C. a regular hexagon?

Complete step-by-step answer:

(A) Since the string forms a square.

       All the sides of a square are of equal length.

       There are 4 sides in a square.

       Length of the string = Perimeter of the square --- (perimeter of a square = 4a)

          ⟹30 cm = 4a --- (Let ‘a’ be the length of each side.)

30/4 = a

7.5 cm = a

(B) Since the string forms an equilateral triangle.

     All the sides of an equilateral triangle are of equal length.

     There are 3 sides in a triangle.

     Length of the string = Perimeter of the triangle --- (perimeter of a triangle = 3a)

     ⟹30 cm = 3a ---- (Let ‘a’ be the length of each side.)

30/3 = a

5 cm = a

(C) Since the string forms a regular hexagon.

     All the sides of a regular hexagon are of equal length.

     There are 6 sides in a hexagon.

     Length of the string = Perimeter of the hexagon --- (perimeter of a hexagon = 6a)

     ⟹30 cm = 6a --- (Let ‘a’ be the length of each side.)

30/6=a

a = 5 cm

Hence, the length of each side of the string to form a square = 7.5 cm.

The length of each side of the string to form an equilateral triangle = 10 cm

The length of each side of the string to form a regular hexagon = 5 cm