Question

What is the length of each side of equalateral triangle if its area is 4√3

Answer 1

Answer:

Let the side of an equilateral triangle be a units.

★ We know that,

$\Rightarrow{\boxed{\bold\red{ Area \: of \: an \: equilateral \: triangle = \frac{ \sqrt{3} }{4} {a}^{2} }}}$

Therefore,

According to the question,

$\Rightarrow{\boxed{\bold\red{ Area \: of \: an \: equilateral \: triangle = 4 \sqrt{3} }}}$

YOUR SOLUTION IS HERE

$\Rightarrow\sf \frac{ \sqrt{3} }{4} {a}^{2} = 4 \sqrt{3} \\ \sf by \: cross - multiplying \: we \: get.... \\ \Rightarrow\sf {a}^{2} = \frac{4 \sqrt{3} \times 4}{ \sqrt{3} } \\ \Rightarrow\sf {a}^{2} = 4 \times 4 \\ \Rightarrow\sf \: a = \sqrt{4 \times 4} \\ \Rightarrow\sf a = 4 \: units.$

Therefore, the side of the equilateral triangle = a = 4 units.

$*\mathbb{IMPORTANT \: FORMULAE:- }*$

RECTANGLE:-

■ Area of a rectangle = length × breadth square units.

■ Perimeter of a square = 2×(length+breadth) unit

SQUARE:-

■ Area of a square = (side) ^2 square units

■ Perimeter of a square = 4×side unit

Triangle:-

■ Area of a triangle = √3/4 a^2 square units

■ Perimeter of a triangle = (sum of all the sides of a triangle) unit

Answer 2

Answer:

$\large\boxed{\sf{4\;\;units}}$

Step-by-step explanation:

Given an equilateral triangle.

Area = 4√3 sq. units

To find the length of each side.

Let the length of each side is ‘a’

We know that, area of equilateral triangle is given by $\dfrac{\sqrt{3}}{4}{a}^{2}$.

Therefore, we get

$= > \frac{ \sqrt{3} }{4} {a}^{2} = 4 \sqrt{3} \\ \\ = > {a}^{2} = 4 \times 4 \\ \\ = > {a}^{2} = 16 \\ \\ = > {a}^{2} = {4}^{2} \\ \\ = > a = 4$

Hence, length of each side is 4 units.