An equilateral triangle a square and a circle have equal perimeters If T denotes the area of the tri...........

Quantitative Aptitude ( CCS) Mensuration 2D

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An equilateral triangle, a square and a circle have equal perimeters. If

T denotes the area of the triangle,

S denotes the area of the square, and

C denotes the area of the circle,

S < T < C

T < C < S

T < S < C

S < C < T

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Explanation:

Explanation: Let p be the perimeter. Then,
Side of equilateral triangle = p/3
Side of square = p/4
Side of circle = p/(2*π)
Now,
Area of equilateral triangle, T = √3/4a² = 1.732/4 * (p/3)² = 0.0481 p²
Area of square, S = (p/4)² = 0.0625 p²
Area of circle, C = π * [p/(2*π)]² = π/4π² p² = 1/4π p² = 0.0796 p²
Clearly, T < S < C.