Question

3.
Find the perimeter of an equilateral triangle given its area is 100rootover3​

Answer 1

A n s w e r

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G i v e n

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• Area of equilateral triangle is 100√3 sq. unit

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F i n d

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• Perimeter of the equilateral triangle

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S o l u t i o n

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Here in this question we are asked to calculate the perimeter of the equilateral triangle

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To calculate perimeter we must know the sides

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So,

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Let the side of equilateral triangle be 's'

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$\underline{\bold{\texttt{Area of equilateral triangle :}}}$

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➠ $\sf A = \sqrt 3 \times \dfrac { a ^2 } { 4 }$ ⚊⚊⚊⚊ ⓵

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Where ,

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• A = Area

• a = Side of square

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$\underline{\bold{\texttt{Area of equilateral triangle :}}}$

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Given that the area of equilateral triangle is 100√3

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• A = 100√3

• a = s

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⟮ Putting the above values in ⓵ ⟯

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➜ $\sf A = \sqrt 3 \times \dfrac { a ^2 } { 4 }$

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➜ $\sf 100 \sqrt 3 = \sqrt 3 \times \dfrac { s^2 } { 4 }$

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➜ $\sf 100 = \dfrac { s^2 } { 4 }$

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➜ s² = 100 × 4

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➜ s² = 400

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➜ $\sf s = \sqrt { 400 }$

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➜ s = 20

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• Hence each side of the equilateral triangle is 20 units

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$\underline{\bold{\texttt{Perimeter of equilateral triangle :}}}$

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➠ 3a ⚊⚊⚊⚊ ⓶

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Where ,

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• a = Side

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$\underline{\bold{\texttt{Perimeter of given equilateral triangle :}}}$

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• a = 20

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⟮ Putting the above value in ⓶ ⟯

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➜ 3a

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➜ 3(20)

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➨ 60 units

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• Hence the perimeter of equilateral triangle is 60 units

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