Question

Area of an equilateral triangle is16 root 3 find the length of each side of the triangle give the solution

Answer 1

$\sqrt{3 } \div 4 \times a {}^{2} { = 16 \sqrt{3} }^{}$
$a { }^{2} = 64 \\ length=a = 8$
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Answer 2

DATA:
Δ= 16√3
a=?
b=?
c=?
 
SOLUTION:
    Let a=b=c = x
∵ 2s = a+b+c
    2s = x + x + x
     2s = 3x
      s = 3x/2

By Using;
    Δ= √s(s-a)(s-b)(s-c)
    Δ= √{3x/2 (3x/2 - x)(3x/2 - x)(3x/2 - x)}
    Δ= √{3x/2 (x/2)(x/2)(x/2)}
    Δ= √(3x⁴/16)
    Δ= √3 x²/4
    16√3 = √3 x²/4
    16√3/√3 = x²/4
    16 = x²/4   
    16×4 = x²
     64 = x²
     √64 = √x²
      x = 8

Hence;
  a = 8
  b = 8
  c = 8