An equilateral triangle, a square and a circle have equal perimeter. If T, S and C denote the area of the triangle, area of the square and area of the circle respectively, then which one of the following is correct?

T < S < C
S < T < C
C < S < T
T < C < S

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 1 : T < S < C

Let the perimeter of triangle, square and circle be equal to ‘x’ cm

Perimeter of equilateral triangle = 3(side) = x

⇒ Side of equilateral triangle = x/3

⇒ Area of equilateral triangle = (√3/4) × (side)² = (√3/4) × (x²/9) = x²/12√3

⇒ T ≅ 0.048x² ...1)

Similarly,

Perimeter of square = 4(side) = x

⇒ Side of square = x/4

⇒ Area of square = (side)² = x²/16

⇒ S = 0.0625x² ...2)

Also,

Perimeter of circle = 2π(radius) = x

⇒ Radius of circle = x/2π

⇒ Area of circle = π(radius)² = π × x²/4π² = x²/4π

⇒ C ≅ 0.0795x² ...3)

∴ Comparing equation (1), (2) and (3), we can write, T < S < C

4 views Answered 2022-09-04 04:29

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