Question

the area of equilateral triangle is 36√3.find its side​

Answer 1

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Area of equilateral triangle =

4

3

(side)

2

∴

4

3

(side)

2

=36

3

(side)

2

=36×4

=9×4×4

=(4×3)

2

side=12cm

perimeter =3×side

=3×12

=36cm

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Answer 2

Solution:

It is given that the area of of an equilateral triangle is 36√3 cm².

We have to find the measure of one side of the equilateral triangle.

The main formula to be used is the equilateral triangle area formula which is derived from the Heron's formula:

$\sf{\implies\:Area\:of\:an\:equilateral\:triangle=\dfrac{\sqrt3}{4}a^2}$

Here, we know the area as 36√3 cm².

Substituting this value into the equation:

$\sf{\longrightarrow\dfrac{\sqrt3}{4}a^2=36\sqrt3}$

Moving the constant to the RHS:

$\sf{\longrightarrow\:a^2=36\sqrt3\times\dfrac{4}{\sqrt3}}$

Cancelling the √3 which constitutes as the numerator and the denominator:

$\sf{\longrightarrow\:a^2=36\times4}$

$\sf{\longrightarrow\:a^2=144}$

$\sf{\longrightarrow\:a=\sqrt{144}}$

$\sf{\longrightarrow\:a=12\:cm}$

Hence, the side of the equilateral triangle measures 12 cm.

Equilateral triangle Area formula:

The equilateral triangle area formula is derived from the Heron's formula to find the area of any triangle whose all the three sides have equal measure.

The formula, as said before is as follows:

$\sf{\implies\:Area\:of\:an\:equilateral\:triangle=\dfrac{\sqrt3}{4}a^2}$

Here, the variable a denotes the side of the equilateral triangle.