Question

if the area of an equilateral triangle is 81√3 .find its perimeter

Answer 1

1) area of an equilateral triangle= 81root3 (root3)/4*a^2= 91 root3 Here a is side a^2= (81*root3*4)/(root3) a^2= 81*4 a^2=(324) a^2=(18)^2 a =18 2) perimeter = 3a =3*18 =54 units

Answer 2

We know that

Area of equilateral triangle = √3/4 (side)2

Substituting the values

81 √3 = √3/4 (side)2

By further calculation

Side2 = (81 √3 × 4)/ √3

So we get

(side)2 = 81 × 4

side = √(81 × 4)

side = 9 × 2 = 18 cm

So the perimeter of equilateral triangle = 3 × side

= 3 × 18

= 54 cm

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