A piece of string is 30 cm 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?

Solution:

We know that the perimeter of any shape is equal to the sum of its all sides.

(a) Perimeter of square = 30 cm

Side = ?

Perimeter of square = 4 × side

⇒ 30 = 4 × side

⇒ Side = 30 / 4 = 7.5 cm

Therefore, 7.5 cm is the length of each side of the square.

(b) Perimeter of an equilateral triangle = 30 cm

Side = ?

Perimeter of equilateral triangle = 3 × side

⇒ 30 = 3 × side

⇒ Side = 30 / 3 = 10 cm

Therefore, 10 cm is the length of each side of an equilateral triangle.

(c) Regular hexagon's perimeter = 30 cm

Side = ?

Perimeter of a regular hexagon = 6 × side

⇒ 30 = 6 × side

⇒ Side = 30 / 6 = 5 cm

Therefore, 5 cm is the length of each side of a regular hexagon.

NCERT Solutions for Class 6 Maths Chapter 10 Exercise 10.1 Question 11

A piece of string is 30 cm 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?

Summary:

It is given that a piece of string is 30 cm long. We have found that that the length of each side of a square, an equilateral triangle, and a regular hexagon will be 7.5 cm, 10 cm, and 5 cm respectively.

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