Question

If the area of an equilateral triangle is 36√3cm And the length of its side and its
perimeter

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Answer 1

GIVEN :

• AREA OF AN EQUILATERAL TRIANGLE = 36√3 cm²

TO FIND :

• LENGTH OF SIDE AND PERIMETER

SOLUTION :

AREA OF EQUILATERAL TRIANGLE = 36√3 cm²

$= > \frac{ \sqrt{3} {a}^{2} }{4} = 36 \sqrt{3 } \\ \\ = > \frac{ {a}^{2} }{4} = 36 \\ \\ = > {a}^{2} = 144 \\ \\ = > a = \sqrt{144} = 12 \: cm$

PERIMETER OF EQUILATERAL TRIANGLE = 3a

$= 3 \times 12 = 36cm$

∴ THE SIDE OF EQUILATERAL TRIANGLE IS 12 cm AND PERIMETER = 36 cm

HOPE IT HELPS !!!!

Answer 2

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⏹ Required Answer:

✏ GiveN:

• Area of equilateral triangle = $\large{\rm{36 \sqrt{3}}}$

✏ To finD:

• Length of its side
• And, perimeter of the equilateral triangle.

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⏹ How to solve?

Equilateral triangle is a triangle with all sides and angles equal, There is a direct formula to find the area of equilateral triangle when side is given.

$\large{ \cdot{ \underline{ \rm{ \purple{Area \: of \: equilateral \: \triangle}}}}} \\ \\ \large{ \rm{ = \frac{ \sqrt{3} }{4} \times {(side)}^{2} }}$

And

$\large{ \cdot{ \underline{ \rm{ \purple{Perimeter \: of \: equilateral \: \triangle}}}}} \\ \\ \large{ \rm{ = 3 \times side}}$

The area formula or direct formula for area of equilateral triangle is derived from heron's formula only. Perimeter is 3 × side, because all the sides of a equilateral triangle is equal.

By using this formula, let's solve this question.

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⏹ Solution:

Given,

• Area of equilateral triangle = $\large{\rm{36 \sqrt{3}}}$

By using formula,

$\large{ \rm{ \longrightarrow \: Area \: of \: eq. \triangle = 36 \sqrt{3} {cm}^{2} }} \\ \\ \large{ \rm{ \longrightarrow \: \frac{ \sqrt{3} }{4} \times {side}^{2} = 36 \sqrt{3} {cm}^{2} }} \\ \\ \large{ \rm{ \longrightarrow \: {side}^{2} = \frac{36 \cancel{\sqrt{3} } \times 4}{ \cancel{\sqrt{3}} } {cm}^{2} }} \\ \\ \large{ \rm{ \longrightarrow \: {side}^{2} = 6 \times 6 \times 2 \times 2 \: {cm}^{2} }} \\ \\ \large{ \rm{ \longrightarrow \: \boxed{ \red{ \rm{ side = 12 \: cm}}}}}$

Now, we have got the side of the equilateral triangle, we can find the perimeter of the equilateral triangle.

By using formula,

$\large{ \rm{ \longrightarrow \: Perimeter \: of \: eq. \: \triangle = 3 \times side}} \\ \\ \large{ \rm{ \longrightarrow \: Perimeter \: of \: eq. \: \triangle = 3 \times 12 \: cm}} \\ \\ \large{ \rm{ \longrightarrow \: \boxed{ \red{ \rm{Perimeter \: of \: eq. \: \triangle = 36 \: cm}}}}}$

Hence, our side is 12 cm and perimeter of eq. triangle = 36 cm

$\large{ \therefore{ \underline{ \underline{ \purple{ \rm{Hence \: solved \: \dag}}}}}}$

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