Question

Find the length of the side of an equilateral triangle whose area is 9√3cm^2

Answer 1

$\boxed{ \bold{ \: area \: of \: equilateral \: triangle \: = \frac{ \sqrt{3} }{4} \times {side}^{2} }}$





Here, Area is given so Putting the value of area in the given formula,



$= > 9 \sqrt{3} = \frac{ \sqrt{3} }{4} \times {side}^{2} \\ \\ \\ = > \frac{9 \times \sqrt{3} \times 4}{ \sqrt{3} } = {side}^{2} \\ \\ \\ = > \sqrt{9 \times 4} = side \\ \\ \\ = > \sqrt{ {3}^{2} \times {2}^{2} } = side \\ \\ \\ = > 3 \times 2 = side$


=> 6 = side





Hence, side of the given equilateral triangle is 6 cm

Answer 2

as we know that the area
of equilateral triangle

= √3 / 4 a^2

so now,

√3 / 4 a^2 = 9 √3

√3 /√3 a^2 = 9×4

a^2 = 36

a = 6 CM

hence,lenght of one side of an equilateral triangle= 6 CM

hope it helps !
thank you !