Question

The area of an equilateral triangle is 6√3 m2 find its parameter solve it clearly​

Answer 1

Given :

• Area of equilateral Δ = 6√3$\sf m^2$

To Find :

• Perimeter of the equilateral Δ

Solution :

Area of equilateral Δ = $\sf 6 \sqrt{3}m^2$

Let the Side of the equilateral Δ=S metre

Area of Equilateral Δ = $\sf \Big(\dfrac{\sqrt{3}}{4}\Big)S^2m^2$

$\implies \sf 6 \sqrt{3}m^2=\Big(\dfrac{\sqrt{3}}{4}\Big) S^2m^2$

$\implies\sf 6 {\cancel{\sqrt{3}}}\Big(\dfrac{4}{{\cancel{\sqrt{3}}}}\Big) =S^2$

$\implies \sf S^2 = 6 \times 4$

$\implies\sf S^2 = 24m$

$\implies\sf S = \sqrt{24}m$

$\implies\sf S = 2\sqrt{6}m$

Perimeter of Δ = $\sf 3 \times side$

$\rightarrow \sf 3 \times 2\sqrt{6}$

$\rightarrow \sf 6 \sqrt{6}m$

________________________________

Required Answer :

Perimeter of the given equilateral Δ is $\underline{ \sf 6 \sqrt{6}m}$

________________________________