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GATE 2018 ME (ME2) – Question 4

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

A circle, square and equilateral triangle have equal perimeters. Which statement is true?

  1. The circle has the largest area.
  2. The square has the largest area.
  3. The equilateral triangle has the largest area.
  4. All three have equal area.

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Show answer and explanation

Correct answer: (A) The circle has the largest area.

Explanation

Let the common perimeter be P. Areas are $P^2/(4\pi)$ for the circle, $P^2/16$ for the square and $\sqrt3P^2/36$ for the equilateral triangle. Their coefficients are 0.07958, 0.06250 and 0.04811. The circle has the largest area: **A**.