Question

An equilateral triangle area is $8$ $m{m}^2$ and its circumcircle radius is $2$ mm. What is the one side of the triangle?

• A. $5$ mm
• B. $6$ mm
• C. $7$ mm
• D. None of these

Answer 1

The correct option is D None of these

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