Question
If the area of an equilateral triangle is 9√3 cm2. What is the length of the side of the triangle.
Answer: Option D
:
D
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D
Let the side of the equilateral triangle = a cm.
Semi Perimeter, s = 3a2
s−a=3a2−a=3a−2a2=a2
Now by heron’s formula
Area of the triangle= √s(s−a)(s−b)(s−c)
⇒9√3=√3a2×a2×a2×a2
⇒√243=√3a416
Squaring both sides,
⇒243=3a416
⇒a4=81×16
⇒a=6 cm
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