What is the length of each side of an equilateral triangle having an a

1.	What is the length of each side of an equilateral triangle having an area of 4 underroot 3square cm
Answer» ANSWER:- Length of each side = 4 cm $\rule{200}{1}$ ⋆ 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)]

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

Answer»

ANSWER:-

Length of each side = 4 cm

$\rule{200}{1}$

⋆ 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)]