Question

The length of the circumference of a circle equals the perimeter of a triangle of equal sides and also the perimeter of a square. The figure coveredleast area will be………………..

Answer 1

Answer:

Solution

The correct option is B c> s > t

Option (C) is the correct answer. Check the video for the approach.

Answer 2

The figure covered least area will be Triangle  if The length of the circumference of a circle equals the perimeter of a triangle of equal sides and also the perimeter of a square

Solution:

Circumference of circle = 2π (radius)

Perimeter of Equilateral Triangle = 3 ( side)

Perimeter of square = 4 ( side)

Area of circle =  π (radius)²

Area of Equilateral Triangle = √3 ( side)² / 4

Area of square =   ( side)²

Step 1:

Assume that Circumference of circle = Perimeter of Triangle = Perimeter of Square = P

Step 2

Find radius of circle from circumference and then find area of the circle

2π (radius) = P  

=> radius  = P/2 π

Area of circle =  π (radius)²

= π (P/2 π)²

= P²/4π

≈ 0.08P

Step 3:

Find side of Equilateral triangle from perimeter and then find area of the triangle

3 (side) = P  

=> side  = P/3

Area of Triangle = √3 ( side)² / 4

= √3 ( P/3)² / 4

= √3 P² / 36

≈ 0.05P

Step 4:

Find side of square from perimeter and then find area of the square

4 (side) = P  

=> side  = P/4

Area of Square =   ( side)²  

=  ( P/4)²  

=  P² / 16

= 0.0625P

Hence 0.05P < 0.0625P < 0.08P

Hence Triangle covered  the least area and Circle Covered maximum area