The plane curve of fixed perimeter and maximum area is
Answers
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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