The area of a circle inscribed in an equilateral triangle is 154cm². Find the perimeter of the triangle.
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please write the steps

Question

The area of a circle inscribed in an equilateral triangle is
154cmÂ² Find the perimeter of the triangle
rn
please write the steps

Ankush Jain · Accepted Answer

Î”ABC is an equilateral triangle Let AB = BC = CA = x cm

â‡’ BD = CD = $\frac{BC}{2} = \frac{x}{2} cm$ Suppose the radius of the inscribed circle be r cm Area of the inscribed circle = 154 cm2 (Given) $∴ π r^{2} = 154 {cm}^{2} \Rightarrow \frac{22}{7} \times r^{2} = 154 {cm}^{2} \Rightarrow r^{2} = \frac{154 \times 7}{22} {cm}^{2} = 49 {cm}^{2} \Rightarrow r = 7 cm$ In Î”BOD, $\tan 30 ° = \frac{OD}{BD} ∴ \frac{1}{\sqrt{3}} = \frac{7 cm}{BD} \Rightarrow BD = 7 \sqrt{3} cm \Rightarrow BC = 2BD = 2 × 7 \sqrt{3} cm = 14 \sqrt{3} cm ∴ Perimeter of Δ ABC= 3 × Side of the equilateral triangle = 3 × BC = 3 × 14 \sqrt{3} cm = 42 \sqrt{3} cm$

The area of a circle inscribed in an equilateral triangle is 154cm². Find the perimeter of the triangle.rnplease write the steps

The area of a circle inscribed in an equilateral triangle is 154cm². Find the perimeter of the triangle.
rn
please write the steps