Question

3. The length of each side of an equilateral triangle
having an area of 9✓3 cm2 is​

Answer 1

Question

the length of each side of an equilateral triangle having an area of 9 root 3 cm square is

Answer

What is given here ?

• it is given here that the the area of the equilateral triangle is 9 root 3 cm square .

what we have to find here ?

• when we have to find the length of its side of the triangle .

Solution

The area of equilateral triangle is

$9 \sqrt{3} cm ^{2}$

Since the area of equilateral triangle is

$\frac{ \sqrt{3} }{4} {a}^{2}$

So , according to the given question

$\frac{ \sqrt{3} }{4} {a}^{2} = 9 \sqrt{3}$

${a}^{2} = 9 \times 4$

${a}^{2} = 36$

$a = 6cm$

Hence, side of the triangle is 6 cm .

Extra explanation

What is an equilateral Triangle ?

triangle is a triangle in which all three sides have the same length .

Area of equilateral triangle

$\frac{ \sqrt{3} }{4} {a}^{2}$

perimeter of equilateral triangle

3× side of equilateral triangle

number of vertices

=> 3

number of edges

=> 3

internal angle

=> 60°

Answer 2

Answer:

$\sf{Side=6cm}$

Step-by-step explanation:

$\textsf{Area of an Equilateral triangle }\sf{=\dfrac{\sqrt{3}}{4}\times Side^2}$

• Given Area of Equilateral Triangle = $\sf{9\sqrt{3}\:cm^2}$

$\to\sf{9\sqrt{3}\:cm^2}\sf{\:=\dfrac{\sqrt{3}}{4}\times Side^2}$

• Multiplying Both Sides by 4

$\to\sf{4\times9\sqrt{3}\:cm^2}\sf{\:=\sqrt{3}\times Side^2}$

$\to\sf{36\sqrt{3}\:cm^2}\sf{\:=\sqrt{3}\times Side^2}$

• Dividing Both Sides by $\sf{\sqrt{3}}$

$\to\sf{\dfrac{36\sqrt{3}\:cm^2}{\sqrt{3}}}\sf{\:=Side^2}$

$\to\sf{36 \:cm^2}\sf{\:=Side^2}$

• Taking Root on Both Sides

$\to\sf{\sqrt{36 \:cm^2}}\sf{\:=Side}$

$\to\sf{6\:cm}\sf{\:=Side}$

• Switch Sides

$\to\sf{Side=6cm}$