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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

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Migrated from GO Mechanical 5 months ago by Arjun

For a given perimeter circle has the largest area.

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

by Veteran (422k points)
+1

@Arjun sir,

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

+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 (4.9k points)
edited by
0
It is correct- but for a given perimeter circle has the largest area - it is in the definition of circle.