Question

if the area of and equilateral triangle is 64√3cm square,what is its perimeter

Answer 1

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Answer 2

Solution :

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Given :

The area of equilateral triangle is 64√3 cm².

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To Find :

The perimeter of equilateral triangle ,..

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We know that,

Equilateral triangle has equal sides,.

&

Area of equilateral triangle = $\frac{ \sqrt{3}}{4} a^2$ sq.units.

Where a is the length of the side of the equilateral triangle,.

So,

We can say that,

⇒ $\frac{ \sqrt{3} }{4} a^2 = 64 \sqrt{3}$

⇒ $a^2 = 64 \sqrt{3} ( \frac{4}{ \sqrt{3}} )$

⇒ $a^2 = ( \frac{(64 \sqrt{3})4}{ \sqrt{3}} )$

⇒ $a^2 = 64(4)$

⇒ a² = 256

⇒ a = +16 (a is positive,can't be negative,.As length of equilateral triangle can't be in negative),.

Hence,

We know that, lengths are equal (& tringle has 3 sides),.

⇒ 3a units.

⇒ 3 x 16

⇒ 48 cm,.

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