Question

the wire of 264cm is cut into two equal portions. one portion is bent in form of a circle and the other is in the firm of an equilateral triangle. find the ratio of tge areas enclosed by them

Answer 1

As the question says, the wire of length 264 cm is cut into equal portion, each portion would measure = 264/2 cm = 132cm.
The first portion is used to make a circle.
Therefore, circumference of circle = 132 cm.
By the formula 2πr,
r = 21 cm. Therefore, area of circle = π*r*r = 1386 cm^2.
Now the second portion is used to make an equilateral triangle.
Therefore, each side of the the triangle (a)= 132/3 cm = 44 cm. And it's area = {(√3)/4}*a*a = 838.29 cm^2.
And the ratio of areas = 1386/838.29, which is equal to 1.65 and that's the answer.

Answer 2

Length of circumference of circle = 264/2 cm = 132 cm
      radius = 132 /(2π) = 21 cm
      Area = 22/7 * 21² = 1386 cm²

perimeter of equilateral triangle = 264/2 = 132 cm
      side = 132/3 = 44 cm
      Area = √3/4 * 44² cm²

Ratio of  circular area : triangle area = 1386 : 484 √3
                 = 693 : 242 √3 = 1.653