• # question_answer 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? TIPS Here, perimeter of each figure will be equal to length of string i.e. 30 cm. Also, perimeter = Sum of all sides of a figure, since each figure has all sides equal, so to find a side of a figure, divide its perimeter by number of sides.

(a) Here, length of string will be the perimeter of square. $\therefore$ Perimeter of square = 30 cm We know that, a square has 4 equal sides. $\therefore$Perimeter of a square $=4\times$ Length of a side Perimeter of a square 30 Now, Length of one side $=\frac{\text{Perimeter}\,\text{of}\,\text{a}\,\text{square}}{4}=\frac{30}{4}cm=7.5cm$ Hence, length of each side of a square is 7.5 cm. (b) Here, length of string will be the perimeter of an equilateral triangle. $\therefore$ Perimeter of equilateral triangle = 30 cm We know that, an equilateral triangle has 3 equal sides. Perimeter of an equilateral triangle $=3\times$ Length of a Side $\therefore$ Length of a side $=\frac{\text{Perimeter of an equilateral triangle}}{\text{3}}$ $=\frac{30}{3}cm=10cm$ Hence, the length of each side of an equilateral triangle is 10 cm. (c) Here, length of string will be the perimeter of regular hexagon. $\therefore$ Perimeter of regular hexagon = 30 cm We know that, a regular hexagon has 6 equal sides $\therefore$ Perimeter of a regular hexagon $=6\times$Length of one side $\therefore$ Length of a side $=\frac{\text{Perimeter of a regular hexagon}}{\text{6}}$ $=\frac{30}{6}cm=5cm$ Hence, the length of each side of a regular hexagon is 5 cm.