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

(i) a square?

(ii) an equilateral triangle?

(iii) a regular hexagon?

The length of the string = 30 cm

(i) When the string is used to form a square, the perimeter of the square = 30 cm.

Perimeter of square = 4 × side

⇒ 30 = 4 × side

⇒ side = $\dfrac{30}{4}$

⇒ side = 7.5 cm

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

(ii) When the string is used to form an equilateral triangle, the perimeter of the triangle = 30 cm.

Perimeter of equilateral triangle = 3 × side

⇒ 30 = 3 × side

⇒ side = $\dfrac{30}{3}$

⇒ side = 10 cm

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

(iii) When the string is used to form a regular hexagon, the perimeter of the hexagon = 30 cm.

Perimeter of regular hexagon = 6 × side

⇒ 30 = 6 × side

⇒ side = $\dfrac{30}{6}$

⇒ side = 5 cm

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