Question

If the area of an equilateral triangle is 81 root3 cm sq. Find its perimeter
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Answer 1

Answer:

Perimeter of triangle is 54 cm.

Step-by-step explanation:

Given :-

• Area of equilateral triangle = 81√3 cm²

To find :-

• Perimeter

Solution :-

For finding perimeter, we first need to find the side of the triangle.

Since the triangle is equilateral, so we just need to know one side.

But the side in not given, so we focus on what is given.

Area of equilateral triangle

= 81√3 cm²

It is known that,

Area of equilateral triangle

= (√3)/4 × side²

Therefore,

81√3 cm² = √3 / 4 × side²

side² = 81√3 × 4 / √3

Here √3 and √3 get cancelled.

side² = 81 × 4

side² = 9×9 × 2×2

side = √(9×9 × 2×2)

side = 9 × 2

side = 18 cm

Now, we know the side.

Therefore, perimeter of equilateral triangle = 3 × side

= 3 × 18

= 54 cm

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Answer 2

Given,

$area \: of \: equilateral \: triangle \: is \: 81 \sqrt{3} cm \: square.$

$then \: the \: perimeter \: of \: triagle \: is \: how \: much.$

$area \: of \: equilateral \: triangle \: = \frac{ \sqrt{3} }{4} {a}^{2}$

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

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

$here \: \sqrt{3} \: and \sqrt{3} will \: get \: cancel.$

${a}^{2} = 81 \times 4$

${a}^{2} = 324$

$a = \sqrt{324}$

$a = 18$

$perimeter \: of \: equilateral \: triangle \: is \: 3a.$

$= 3 \times 18$

$= 54cm$

Therefore the perimeter of the triangle is 54cm.

Note: Formulas :

Area of equilateral triangle =  √3a^2/4.

Perimeter of equilateral triangle = 3a.

In the above formula a = side.

We require side of a equilateral triangle to find out the area or perimeter.