Question

the length of each side of an equilateral triangle having an area of 9 root 3 cm^2

Answer 1

As per the data given in the above question,

The given data is area of triangle i.e. $9\sqrt{3}$

Here we have to find the length of an equilateral triangle.

By using the formula of area of equilateral triangle we are going to find the length of equilateral triangle.

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

where a is the side of an equilateral triangle.

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

Substitute the value in above equation we get,

$9\sqrt{3}=\frac{\sqrt{3} }{4} a^2\\9\sqrt{3} \times \frac{4}{\sqrt{3} } =a^2\\36=a^2$

Taking the root we get,

$a=\sqrt{36} \\a=6\: cm$

Hence the length of each side of an equilateral triangle is $6\: cm.$

Answer 2

Answer:

The length of each side of equilateral triangle is 6 cm.

Step-by-step explanation:

As per the data given in the question,

area of the equilateral triangle is$9\sqrt{3}\: cm^{2}$

We know that formula of area of equilateral triangle is $\frac{\sqrt{3}}{4}a^{2}$where a is the side of triangle.

So, equating both,

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

$a^{2}=36\\ a=6\: cm$

Therefore, the length of each side of equilateral triangle is 6 cm.

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