A piece of wire 132 cm long is bent successively in the shape of an equilateral triangle, a square and a circle. Then area will be largest in shape of:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. Circle
Case I:
Perimeter of Equilateral triangle = 132 cm
⇒ 3x = 132
⇒ x = 44
Area of equilateral triangle = √3/4 (44)2 = 837.32 cm2
Case II:
Perimeter of square = 132 cm
⇒ 4x = 132
⇒ x = 33 cm
Area of square = x2 = 332 = 1089 cm2
Case III:
Perimeter of circle = 132 cm
⇒ 2πr = 132
⇒ 2 × 22/7 × r = 132
⇒ r = 21 cm
Area of circle = πr2 =22/7 × 212 = 1386 cm2
Hence, area will be largest in shape of Circle.