Question

What is the length of each side of an equilateral triangle having an area of4√3 cm².

Answer 1

$\huge\boxed {Answer}$

As all we know that

Area of equilateral ∆ = (√3/4)*a²

4√3 = (√3/4)*a²

4 = a²/4

a² = 16

a = √16 = 4 cm

Result :-

Length of the each side of an equilateral

triangle is 4 cm .

Answer 2

Answer:-

Area of Equilateral traingle = 4√3 cm²

\frac{ \sqrt{3} }{4} \times (side) {}^{2} = 4 \sqrt{3 } \\ \\ {(side)}^{2} = 4 \sqrt{ 3} \times \frac{4}{ \sqrt{ 3 } } \\ \\ {(side)}^{2} = 4 \times 4 \\ \\ (side) {}^{2} = (4)^2 \\ \\ = > side = 4 \: cm

HENCE,

Length of side of given equilateral triangle is 4 cm.


OR


Let the Length of side of equilateral triangle = a (cm)

Area of equilateral triangle = ✓3/4 × (a)²

4✓3 = ✓3/4 × a²

a² = 4✓3 × 4 / ✓3

a² = 4 × 4

a² = 16

a = ✓16 = 4 cm


Hence,

The Length of side of an equilateral triangle = a = 4 cm

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