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The perimeters of a circle, a square and an equilateral triangle are same and their areas are C, S and T respectively. Which of the following statement is true ?
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- C = S = T
- C > S > T
- C < S < T
- S < C < T
- C = S = T
Correct Option: B
Radius of circle = x cm.
Side of square = y cm.
Side of equilateral triangle = z cm.
Circumference of circle = Perimeter of square = Perimeter of equilateral triangle
⇒ 2πx = 4y = 3z
| ⇒ x = | = | z = | |||
| 2π | π | 3 |
Area of circle ‘C’ = πx²
| = π × | y² = | y² > y² | ||
| π² | π |
Area of square ‘S’ = y²
| Area of triangle ‘T’ = | z² | |
| 4 |
| = | × | y² | ||
| 4 | 3 × 3 |
| = | y² < y² | |
| 3√3 |
∴ T < S < C
