Question

find the perimeter of an equilateral triangle,if it's area is 64 √3 cm2
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Answer 1

area of equilateral triangle is √3/4*side square

so 64√3=√3/4side sq

therefore by solving we get side =16
so perimeter =48cm

Answer 2

Answer:

The formula for area of the triangle is

$\sqrt{s \times (s - a) \times (s - b) \times (s - c)}$

Where s= a+b+c/2 . As it is a equilateral triangle so a=b=c hence s=3a/2 Hence area of the triangle is

$\sqrt{1.5a \times 0.5a \times 0.5a \times 0.5a}$

So Area of the triangle is

$\frac{ \sqrt{3} a ^{2} }{4}$

It is given that area of the triangle is 64√3 square centimetre .So

64√3 =>√3*a*a/4 => 64*4*√3/√3 = a*a

So a*a = 256 Hence the length of each side of the triangle is 16cm. Perimeter of an equilateral triangle is 48 cm . Hope it helps you.