Question

length of each side of a equalaterial triangle of area 4√3​

Answer 1

GIVEN :-

• Area of equilateral ∆ = 4√3 units².

TO FIND :-

• Length of each side of equilateral ∆.

SOLUTION :-

$\\ \ : \implies \displaystyle \sf \: Area \: of \: Equilateral \: \triangle = \frac{ \sqrt{3} }{4} \bigg (side \bigg) ^{2}$

$: \implies \displaystyle \sf \: 4 \sqrt{ 3} = \frac{ \sqrt{3} }{4} \bigg (side \bigg) ^{2}$

$: \implies \displaystyle \sf \: 4 \times 4 \sqrt{3} = \sqrt{3} \times \bigg (side \bigg) ^{2}$

$: \implies \displaystyle \sf 16 \sqrt{3} = \sqrt{3} \times \bigg(side \bigg) ^{2}$

$: \implies \displaystyle \sf \bigg(side \bigg) ^{2} = \frac{16 \sqrt{3} }{ \sqrt{3} }$

$: \implies \displaystyle \sf \bigg(side \bigg) ^{2} = 16$

$: \implies \displaystyle \sf side = \sqrt{16}$

$: \implies \displaystyle \sf side = \sqrt{4 ^{2} }$

$: \implies \underline{ \boxed{\displaystyle \sf side = 4 \: units.}}$

$\therefore \underline{\displaystyle \sf Length \ of \ each \ side \ of \ equilateral \ \triangle \ is \ 4 \ units}$

Answer 2

Given:

• Area of Equilateral Triangle = 4√3 sq units

Find:

• Length of each side of Triangle = ?

Solution:

Here, area of sq. is 4√3 sq units

Then, let the sides of the triangle be x

Now, we, know that

$\underline{ \boxed{ \sf Area \: of \: triangle = \frac{ \sqrt{3} }{4} \times {a}^{2} }}$

where,

• area of triangle = 4√3 sq units
• side of triangle a = x

So,

$\sf \to Area \: of \: triangle = \frac{ \sqrt{3} }{4} \times {a}^{2}$

$\sf \implies 4 \sqrt{3} = \frac{ \sqrt{3} }{4} \times {(x)}^{2}$

$\sf \implies \frac{4 \sqrt{3} \times 4}{ \sqrt{3} } = {x}^{2}$

$\sf \implies \frac{ 16\sqrt{3}}{ \sqrt{3} } = {x}^{2}$

$\sf \implies 16 = {x}^{2}$

$\sf \implies x = \sqrt{16}$

$\sf \implies x = \sqrt{ {(4)}^{2} }$

$\underline{\boxed{\sf \to x = 4units}}$

__________________

Hence, the length of each side of the given equilateral triangle will be 4units