Question

Find the length of equilateral triangle having an area 9√3 cm2

Answer 1

given area of equilateral triangle = 9√3 cm^2

as we know that , area of equilateral triangle

= √3 / 4 ( side)^2.

let side = a

so now ,

√3 / 4 (a)^2 = 9√3

a^2 = 4 ×9 √3 / √3

a^2 = 36

a = 6 cm

hence ,the length of equilateral triangle (a) = 6 cm

Answer 2

Answer:

$\sf{Side=6cm}$

Step-by-step explanation:

$\textsf{Area of an Equilateral triangle }\sf{=\dfrac{\sqrt{3}}{4}\times Side^2}$

• Given Area of Equilateral Triangle = $\sf{9\sqrt{3}\:cm^2}$

$\to\sf{9\sqrt{3}\:cm^2}\sf{\:=\dfrac{\sqrt{3}}{4}\times Side^2}$

• Multiplying Both Sides by 4

$\to\sf{4\times9\sqrt{3}\:cm^2}\sf{\:=\sqrt{3}\times Side^2}$

$\to\sf{36\sqrt{3}\:cm^2}\sf{\:=\sqrt{3}\times Side^2}$

• Dividing Both Sides by $\sf{\sqrt{3}}$

$\to\sf{\dfrac{36\sqrt{3}\:cm^2}{\sqrt{3}}}\sf{\:=Side^2}$

$\to\sf{36 \:cm^2}\sf{\:=Side^2}$

• Taking Root on Both Sides

$\to\sf{\sqrt{36 \:cm^2}}\sf{\:=Side}$

$\to\sf{6\:cm}\sf{\:=Side}$

• Switch Sides

$\to\sf{Side=6cm}$