Question

A piece of string is 30cm long. What will be the length of each side if the string is used to form-
$$\begin{gathered} \text{A}\text{. a square?} \\ \text{B}\text{. an equilateral triangle?} \\ \text{C}\text{. a regular hexagon?} \end{gathered}$$

Answer 1

Hint: To solve the given question we equate the perimeter of the figure to the length of the string. Using the formula of perimeter we calculate the length of the sides of the figure.

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.)
           ⟹${\displaystyle \frac{30}{4}}$ = a
           ⟹a = 7.5 cm

(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.)
      ⟹${\displaystyle \frac{30}{3}}$ = a
      ⟹a = 10 cm

(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.)
      ⟹${\displaystyle \frac{30}{6}}$= 6a
      ⟹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

Note – In order to solve this type of question the key is to identify the length of the string to be equal to the perimeter. Then we equate the given length of the string to the perimeter and check for the length of the side.