Question

the perimeter of an equilateral triangle of area 64 under root 3 cm square

Answer 1

let the side of an equilateral triangle be a

Area = 64√3 cm^2

√3/4*a^2 = 64√3

a^2 = 64*4

a = 16 cm

hope it helped you

Answer 2

Answer:

48 cm's

Step-by-step explanation:

Given:- Area of an Equilateral triangle = $64\sqrt{3} cm^{2}$.

To find:- Perimeter of the Equilateral triangle.

Solution:-

As we know, Area of an equilateral triangle = $\frac{\sqrt{3}}{4} a^{2}$, where a = each side of an equilateral triangle.

∴ $\frac{\sqrt{3}}{4} a^{2}$ =  $64\sqrt{3}$

⇒ $a^{2} = \frac{4 * 64\sqrt{3} }{\sqrt{3}}$

⇒ $a^{2}$ = 4 × 64

⇒ $a^{2}$ = 2×2×8×8

⇒ a = +16, -16

Since sides of a triangle can never be negative.

∴ a = 16.

As we know, Perimeter is equal to Sum of all sides

∴ Perimeter of an Equilateral triangle = 3a, where a = each side of an equilateral triangle.

⇒ Perimeter = 3 × 16 cm's.

                     = 48 cm's

Therefore, Perimeter of an equilateral triangle whose Area = $64\sqrt{3} cm^{2}$ is 48 cms.

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