Question

An equilateral triangle, a square and a circle have equal perimeters. If t denotes the area of the triangle, s denotes the area of the square and c denotes the area of the circle , then

Answer 1

Answer:

t : s : c :::  1/3√3  : 1/4  :  1/π

Step-by-step explanation:

An equilateral triangle, a square and a circle have equal perimeters. If t denotes the area of the triangle, s denotes the area of the square and c denotes the area of the circle , then

Let say Perimeter = P

then Sides of an equilateral Triangle = P/3

Area of an equilateral triangle = (√3 / 4)(P/3)² = t

=> t = P²/12√3

Sides of a square = P/4

Area of a square = (P/4)² = s

=> s = P²/16

radius of circle = P/2π

Area of Circle = π (P/2π)² = c

=> c = P²/4π

=> t : s : c :::  P²/12√3 : P²/16  : P²/4π

=> t : s : c :::  1/3√3  : 1/4  :  1/π

Answer 2

Answer:

here are your answer

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