Question

find the measure of each side of the equilateral triangle if its area is 256root 3 cm square​

Answer 1

Answer:      32 cm

Step-by-step explanation:

area of equilateral triangle = √3 /4 ×a²

∴  √3 /4 a² = 256√3

or,      a²     = 256×4

or,      a       = 32

Hence, the each side of the equilateral triangle is 32 cm

Answer 2

Step-by-step explanation:

area of an equilateral triangle √3a square÷2

given that √3a square÷4=256√3cm square.

a=256×√3×4÷√3

1024×√3÷√3

rationalising denominator

1024√3×√3÷√3×√3

=1024×3÷3

1024=÷3

= 34.13cm

Consider x as the side of equilateral triangle.

As triangle has 3 sides,

x+x+x=34.13

3x=34.13

x=34.13÷3

x= 11.37666666......cm

which is equal to x= 11 CM ( approximately).