Question

What is the length of each side of an equilateral triangle having an area of 4 underroot 3square cm

Answer 1

AnswEr:-

Length of each side = 4 cm

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⋆ DIAGRAM:-

$\setlength{\unitlength}{0.78 cm}\begin{picture}(12,4)\thicklines\put(5.4,5.8){ A }\put(11.2,5.8){ B }\put(8.4,10){ C }\put(6,6){\line(2,3){2.5}}\put(11,6){\line(-2,3){2.5}}\put(6,6){\line(1,0){5}}\put(5,7.9){ 4\:cm }\put(11,7.9){ 4\:cm }\put(8,5){ 4\:cm }\end{picture}$

Given:-

• Area of equilateral∆ = 4√3 cm²

To find:-

• Side of equilateral∆ = ?

Solution:-

As the triangle is equilateral, we know:-

☛ $\boxed{\boxed{\sf\blue{Area \: of \: equilateral \: \triangle = \dfrac{\sqrt{3}}{4}\: a^2 }}}$

Here, a = length of each equal sides.

• Putting values:-

$\dashrightarrow\sf 4\sqrt{3} = \dfrac{\sqrt{3}}{4}\: a^2 \\\\\dashrightarrow\sf \dfrac{\sqrt{3}a^2}{4} = 4\sqrt{3} \\\\\dashrightarrow\sf a^2 = 4\sqrt{3}\times \dfrac{4}{\sqrt{3}}\\\\\dashrightarrow\sf a^2 = 4 \times 4 \\\\\dashrightarrow\sf a^2 = 16 \\\\\dashrightarrow\sf a = \sqrt{16}\\\\\dashrightarrow{\boxed{\sf{a = \large{\boxed{\sf\green{4 \: cm }}} }}}$

Therefore,

Side of equilateral∆ = 4 cm

More formulas:-

↠Area of isosceles∆ = (b/4)√(4a² - b²)

↠Area of non-equal sides ∆ = √[s(s - a)(s - b)(s - c)]

Answer 2

Given :

• Area of the equilateral triangle = 4√3.

To find :

• Length of the equilateral triangle =?

Step-by-step explanation:

Area of the equilateral triangle = 4√3. [Given]

We know that,

Area of the equilateral triangle = √3/4 side²

Substituting the values in the above formula, we get,

➟ 4√3 = √3/4 side²

➟ side² = 4√3 × 4 /√3

➟ side² = 4 × 4

➟ side² = 16

➟ side = √16

➟ side = √4× 4

➟ side = 4.

We know that the sum of the all sides of the equilateral triangle have equal lenght.

So, The length of the equilateral triangle= 4 cm.

Verification :

Area of the equilateral triangle = 4√3. [Given]

Length of the equilateral triangle = 4cm.

We know that,

Area of the equilateral triangle = √3/4 side²

Substituting the values, we get,

➟ 4√3 = √3/4 × 4²

➟ 4√3 = √3/4 × 16

➟ 4√3 = 4√3

L.H.S = R. H. S

Hence, it is verified.