Math, asked by naricassa970, 5 months ago

The plane curve of fixed perimeter and maximum area is

Answers

Answered by amitnrw
1

The plane curve of fixed perimeter and maximum area is CIRCLE

Step-by-step explanation:

Lets take Example

Perimeter  = 12

Equilateral Triangle side = 12/3 = 4

=> area = (√3/ 4) 4²  = 4√3  = 6.93   sq unit

Square side = 12/4 = 3

Area = 3²  = 9 sq units

Hexagon  Side = 12/6 = 2 m

Area =  6  (√3/ 4) 2² =  6√3  = 10.39   sq unit

as number of sides keep increasing area keep increasing  

Circle can be considered as with infinite sides

Circumference of circle = 2π(radius)

2π(radius)  = 12

=> radius = 6/π

Area of circle = π (radius)²

= π  (6/π)²

= 36/ π

= 11.46  sq unit

The plane curve of fixed perimeter and maximum area is Circle

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