Question

if area of an equalilateral triangle
$2 \sqrt{3}$
${cm}^{2}$
,its perimeter will be​

Answer 1

Answer:

$6\sqrt{2} \: cm$

Step-by-step explanation:

Area of an equilateral triangle:

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

, where a is the length of the side.

Here,

$area = 2 \sqrt{3} \: {cm}^{2} \\ \frac{ \sqrt{3} }{4} a^{2} = 2 \sqrt{3} \: {cm}^{2} \\ a^{2} = 2 \sqrt{3} \times \frac{4}{ \sqrt{3} } \: {cm}^{2} \\ {a}^{2} = 8 \: {cm}^{2} \\ a = \sqrt{8} \: cm = 2 \sqrt{2} \: cm \\ side = 2 \sqrt{2} \: cm$

Perimeter of equilateral triangle = 3a

$3a = 3 \times 2 \sqrt{2} \: cm = 6 \sqrt{2} \: cm \\ Perimeter = 6 \sqrt{2} \: cm$

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Answer 2

Answer:

6

2

cm

Step-by-step explanation:

Area of an equilateral triangle:

34a2\frac{ \sqrt{3} }{4} {a}^{2}

4

3

a

2

, where a is the length of the side.

Here,

area=23cm234a2=23cm2a2=23×43cm2a2=8cm2a=8cm=22cmside=22cm\begin{lgathered}area = 2 \sqrt{3} \: {cm}^{2} \\ \frac{ \sqrt{3} }{4} a^{2} = 2 \sqrt{3} \: {cm}^{2} \\ a^{2} = 2 \sqrt{3} \times \frac{4}{ \sqrt{3} } \: {cm}^{2} \\ {a}^{2} = 8 \: {cm}^{2} \\ a = \sqrt{8} \: cm = 2 \sqrt{2} \: cm \\ side = 2 \sqrt{2} \: cm\end{lgathered}

area=2

3

cm

2

4

3

a

2

=2

3

cm

2

a

2

=2

3

×

3

4

cm

2

a

2

=8cm

2

a=

8

cm=2

2

cm

side=2

2

cm

Perimeter of equilateral triangle = 3a

3a=3×22cm=62cmPerimeter=62cm\begin{lgathered}3a = 3 \times 2 \sqrt{2} \: cm = 6 \sqrt{2} \: cm \\ Perimeter = 6 \sqrt{2} \: cm\end{lgathered}

3a=3×2

2

cm=6

2

cm

Perimeter=6

2

cm