An equilateral triangle a square and a circle have equal perimeter If T S and C denote the area of t...........

Quantitative Aptitude (CDS) Mensuration 2D

An equilateral triangle, a square and a circle have equal perimeter. If T, S and C denote the area of the triangle, area of the square and area of the circle respectively, then which one of the following is correct?

T < S < C

S < T < C

C < S < T

T < C < S

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Explanation:

Let a be the side of square
Let l be the side of equilateral triangle.
Let r be the radius of circle.
Let P be the perimeter of each one.
For square P = 4a
For triangle P = l x 3
L = P/3

$Area =\frac{\sqrt{3}}{4}\left ( \frac{P}{3} \right )^{2}=\frac{P^{2}}{12\sqrt{3}} = \frac{P^{2}}{20.78}$