# QA – Placement Quizzes | Mensuration 2D | Question 13

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,

then:**(A)** S < T < C**(B)** T < C < S**(C)** T < S < C**(D)** S < C < T**Answer:** **(C)****Explanation:** Let p be the perimeter. Then,

Side of equilateral triangle = p/3

Side of square = p/4

Side of circle = p/(2*Pi)

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 = Pi * [p/(2*Pi)]² = Pi/4Pi² p² = 1/4Pi p² = 0.0796 p²

Clearly, T < S < C.

Quiz of this Question

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