Question

The area of an equilateral triangle is 16 √3 sq.m. find its perimeter

Answer 1

Answer:

Perimeter is 24

Step-by-step explanation:

Area of the equilateral triangle is √3/4 a^2

=> √3/4 a^2 = 16 √3

=> a^2= 64

=> a = 8

The perimeter of equilateral triangle is sum of it's three sides = a+a+a=8+8+8= 24

Answer 2

In the above Question , we have a. equilateral triangle .

We know that -

In an equilateral triangle , all the sides and the angles are equal .

Here , let us assume that each side of the given equilateral triangle is x cm .

Perimeter of the given triangle -

=> 3 x

Semiperimeter of the triangle -

=> [ Perimeter / 2 ]

=> ( 3 x / 2 )

Now , according to Herons Formula -

Area = \sqrt { ( s )( s - a )( s - b )( s - c ) }

Here ,

s - a = s - b = s - c

=> ( 3x / 2 ) - x

=> ( 3x - 2x ) / 2

Substituting this into the formula , we get the area or the equilateral triangle as -

( √3 / 4 ) a .

So ,

( √ 3 / 4 ) a² = 16 √ 3

=> √3 a² = 64 √ 3

=> a² = 64 m

=> a = 8 m

Perimeter

=> 3a

=> 3 × 8 m

=> 24 m .

This is the required answer .

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