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.

Answer:

(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.