An equilateral triangle area is 8 $m m^{2}$ and its circumcircle radius is $2$ mm. Find the perimeter of the triangle.

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Solution

The correct option is A $12$ mm
Circumcircle radius $=$ $\frac{a b c}{4 \times \sqrt{s (s - a) (s - b) (s - c)}}$
Where, area of the triangle $=$ $\sqrt{s (s - a) (s - b) (s - c)}$
$a = b = c$ (Since the triangle is equilateral)
$a b c =$ $a^{3}$
So, $2 \times 4 \times 8 =$ $a^{3}$
$64 =$ $a^{3}$
$a = 4$ mm
One side of the triangle $= 4$ mm
So, perimeter of a equilateral triangle $= 3 \times 4 = 12$ mm

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An equilateral triangle area is 8 mm2 and its circumcircle radius is 2 mm. Find the perimeter of the triangle.

The correct option is A 12 mmCircumcircle radius = abc4×√s(s−a)(s−b)(s−c)Where, area of the triangle = √s(s−a)(s−b)(s−c)a=b=c (Since the triangle is equilateral)abc= a3So, 2×4×8= a364= a3a=4 mmOne side of the triangle =4 mmSo, perimeter of a equilateral triangle =3×4=12 mm

An equilateral triangle area is 8 $m m^{2}$ and its circumcircle radius is $2$ mm. Find the perimeter of the triangle.