Question

The perimeter of an equilateral triangle is
V3 times its area. Find the length of each side.​

Answer 1

Ans ---> Length of each side = 4 unit

Given---> Perimeter of an equilateral

triangle is √ 3 times its area .

Solution---> Let side of equilateral

triangle be 'a' .

Each side of an equilateral triangle is equal so length of each side of equilateral triangle is 'a'.

Perimeter of equilateral Δ = 3 ( side )

= 3 ( a )

= 3 a unit

√3

Area of equilateral Δ = ----- (Side )²

4

√3

= ------- ( a )² unit²

4

ATQ

Perimeter of Δ = √3 ( Area of Δ )

√3

=> 3 a = √3 ------ a²

4

3

=> 3 a = -------- a²

4

3 × 4

=> a = ----------

3

=> a = 4 unit

Length of each side = 4 unit

Additional information --->

1) Area of squqre = Side²

2) Area of rectangle = Length × Breadth

3)Area of triangle = 1 / 2 Base × height

4)Area of circle = π r²

Answer 2

Answer:

Let the side equilateral triangle be = x .

We know that,

Perimeter of equilateral triangle having side x is given by,

$perimeter = 3x$

And

Area of equilateral triangle having side x is given by,

$area = \dfrac{ \sqrt{3} }{4} {x}^{2}$

Here,

Given that,

perimeter is V3 Times its area

i.e.

$perimeter = \sqrt{3} \times area \\ \\ \implies3x = \sqrt{3} \times \frac{ \sqrt{3} }{4} {x}^{2} \\ \\ 3x = \frac{3}{4} {x}^{2} \\ \\ 12x = 3 {x}^{2} \\ \\ 3 {x}^{2} - 12x = 0 \\ \\ 3x(x - 4) = 0 \\ \\ \implies x = 0 \: \: or \: \: x = 4$

As,

length can't be equal to 0

So,

$x \ne0 \\ \\ \implies x = 4$

As x is the side of the triangle so length of each side will be

4 units