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what is the ratio of the areas of a circle and an equilateral triangle whose diameter and a side are respectively equal

Posted by Manav Kumar 4 years, 9 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 4 years, 9 months ago

Given :

Let ‘d’ be the diameter of a circle and ‘a’ be the side of a triangle.

Diameter of a circle = side of equilateral triangle

d = a

Radius of a circle, r = d/2

Area of circle,A1 = πr²

Area of an equilateral ∆, A2 = √3/4 a²

Ratio of the Area of circle and Area of an equilateral ∆ :

A1 : A2 = πr² : √3/4× a²

A1 / A2 = πr² / √3/4 ×a²

A1 / A2 = π(d/2)² / √3/4× a²

A1 / A2 = π(a/2)² / √3/4 × a²

[d = a]

A1 / A2 = π(a²/4) / √3/4 × a²

A1 / A2 = πa²/4 × 4 /√3a²

A1 / A2 = π/√3

A1 : A2 = π : √3

Hence, the Ratio of the Areas of circle and equilateral ∆ is π : √3

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