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,
(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)
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.

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