Question
An equilateral triangle ,a square and a circle have equal perimeters . If T denotes the area of the triangle , S , the area of the square and C , the area of the circle , then :
Answer: Option C
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Let the perimeter of each be a.
Then ,side of the equilateral triangle = `a/3`
Side of the square = `a/4`
radius of the circle = `(a)/(2 pi)`
`:.` T = `sqrt(3)/4 xx (a/3)^2 = (sqrt(3) a^2)/(36)`
S = `(a/4)^2 = a^2/16`
C = `pi xx ((a)/(2 pi))^2 = (a^2)/(4 pi) = (7a^2)/(88)`
So, T < S < C.
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