Question

Take a soft wire. Measure it's length. Make a square, a circle, an equilateral triangle and find their circumference perimeters. Verify that they are equal.​

Answer 1

Answer:

Let the perimeter be p, radius of circle be r and side length of square and triangle be a and b respectively.

p=2πr=4a=3b

so r=p2π,a=p4,b=p3

area of circle = πr2=p24π

area of square = a2=p216

area of triangle = 3√4b2=p2123√

Since 4π<16<12 3–√ , area of circle > square > triangle.

In fact, for a given perimeter, a circle has the largest area of all possible figures

Step-by-step explanation: