Question
The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?
Options :
The circle has the largest area.
The square has the largest area.
The equilateral triangle has the largest area.
All the three shapes have the same area.
Answer :
The circle has the largest area.
Solution :
The perimeter of Circle of radius r = 2πr
The perimeter of a square of side s = 4s
The perimeter of an equilateral triangle of side a = 3a
The perimeters of a circle, a square, and an equilateral triangle are equal.
2πr = 4s = 3a
s = 3/4 a = 0.75 a
r = 3/2π a = 0.477 a
Area of an equilateral triangle:
Atrg = √3a²/4 = 0.433a²
Area of square = s² = (0.75 a)² = 0.5625 a²
Area of Circle = 2πr² = π(0.477 a)² = 0.714 a²
Acircle > ASquare >Atrg
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