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The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements 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 the three shapes have the same area
in Numerical Ability by Veteran
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Migrated from GO Mechanical 1 year ago by Arjun

2 Answers

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Best answer
For a given perimeter circle has the largest area.

Similarly, for a given surface area, a cube has the largest volume.

So, correct answer: A
by Veteran
+1

@Arjun sir,

For given surface area SPHERE has the largest volume, not CUBE..

0
how to prove it analytically ?
+1 vote

Let's take $100$ units as the perimeter

Circle:

  • $2πr = 100$
  • $\implies r = 100/(2π) = 100/(2\times 3.14) = 15.92$ units
  • Area $= πr^2$
  • $=3.14\times 15.92\times 15.92 = 795.82$ square units

Square:

  • $4a = 100$
  • $\implies a = 25 $units
  • Area $= a\times a = 25\times 25 = 625$ square units

Equilateral Triangle:

  • $3s = 100$
  • $s = 100/3 = 33.33$ units
  • Area $=\frac{\sqrt 3 }{ 4}  s^2$
  • $=\frac{\sqrt 3}{4} \times  33.33 \times 33.33$
  • $ = 481.029$ square units

$795.82 > 625 > 481.029$

Circle Area > Square Area > Equilateral Triangle Area

Hence, A is Correct.

by Active
edited by
0
It is correct- but for a given perimeter circle has the largest area - it is in the definition of circle.
Answer:

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