Question

If equilateral triangle has area as 4√3sq.cm then perimeter of triangle is ??????

Answer 1

Given :

• Area of the equilateral triangle = 4√3 cm².

To find :

• Perimeter of the equilateral triangle =?

Step-by-step explanation:

Area of the equilateral triangle = 4√3 cm². [Given]

We know that,

Area of the equilateral triangle = √3/4 side²

Substituting the values in the above formula, we get,

➟ 4√3 = √3/4 side²

➟ side² = 4√3 × 4 /√3

➟ side² = 4 × 4

➟ side² = 16

➟ side = √16

➟ side = √4× 4

➟ side = 4.

We know that the sum of the all sides of the equilateral triangle have equal lenght.

So, The length of the equilateral triangle= 4 cm.

Now,

We have to find the Perimeter of the equilateral triangle,

We know that,

Perimeter of Equilateral triangle = 3a.

Substituting the values in the above formula, we get,

= 4 × 3

= 12

Therefore, Perimeter of Equilateral triangle = 12 cm.

Answer 2

Question :-

If equilateral triangle has area as 4√3sq.cm then what is the perimeter of triangle ?

Given :-

• The area of equilateral ∆ is 4√3 sq.cm.

To find :-

• Perimeter of equilateral ∆.

Solution :-

We know that,

•Equilateral triangle has equal sides .

$Area \: of \: equilateral \: triangle \: = \frac{ \sqrt{3} }{4} {a}^{2} \\ \\ here ,\: a = length \: of \: the \: side \: of \: triangle \: . \\ \\ so ,\\ \implies \frac{ \sqrt{3} }{4} {a}^{2} = 4 \sqrt{3} \\ \\ \implies \: {a}^{2} = 4 \sqrt{3} (\frac{4}{ \sqrt{3} }) \\ \\ \implies {a}^{2} = \frac{4 \sqrt{3} \times 4}{ \sqrt{3} } \\ \\ \implies {a}^{2} = 16 \\ \\ \implies \: a = \sqrt{4 \times 4} \\ \\ \implies \: a = 4$

We know that ,

• Perimeter of equilateral triangle = 3a

Putting a = 4

=> 3 × 4

=> 12

Therefore,

${\purple{\boxed{\large{\bold{Perimeter \: of equ. \: triangle \: = 12 cm }}}}}$