Question

the area of a equrilaterl triangle is 81root3 cmsquar. find its perimeter ​

Answer 1

Question : If the area of a equilateral triangle is 81√3 cm². find its perimeter ?

Solution :

Given : Area of Equilateral = 81√1 cm²

•°• Area of Equilateral = √3/4 × a² , Where a represent Side of Equilateral Triangle.

Now, According to the Question!

⇒ √3/4× a² = √3/4 × a²

$\sf{ \frac{ \sqrt{3} }{4} \times {a}^{2} = \frac{81}{ \sqrt{3} } } \\ \\ \sf{\frac{ \sqrt{3 {a}^{2} } }{4} = \frac{81 }{ \sqrt{3} }} \\ \\ \sf{ 3 {a}^{2} = 81 \times 4} \\ \\ \sf{3 {a}^{2} = 324} \\ \\ \sf{a = 10.4}$

Now, Perimeter of Equilateral Triangle = a + a + a

⇒ 3a

⇒ 3a ⇒ 3 ( 10.4) [ •°• a = 10.4 ]

⇒ 31.2 (approximately )

Therefore , Required Value of perimeter of ∆ is 31.20 .

Answer 2

Given :

The area of equilateral triangle = 81√3 cm²

To Find :

It's Perimeter

Solution :

We know that the area of an equilateral triangle having side a is =

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

Then ,

Here Area = 81√3 cm²

$\frac{ \sqrt{3} }{4} {a}^{2} = 81 \sqrt{3} \\ \\ {a}^{2} = 81 \times 4 \\ \\ = 324 \\ \\ a = 18$

Now ,

Side = 18 cm

Perimeter of an equilateral triangle = 3(side)

= 3(18 cm) = 54 cm