The number of inches in the perimeter of an equilateral triangle equal

The question states that the numerical value of perimeter of the equilateral triangle is equal to the value of the area of the circumscribed circle.

Let side of the triangle be = x

Hence perimeter = 3x

Height of the triangle =\(\sqrt{3}x/2\)

In case of equilateral triangle the height and median are the same lines. And the centroid is also the circumcentre. Hence the centre of the circle will be same as centroid.

We know the median of the triangle is divided by the centroid in the ration 2:1.

So the radius of the circumcircle = \(2/3*\sqrt{3}x/2 = x/\sqrt{3}\)...i)

\(Area = \pi(x/\sqrt{3}) ^2\)

From question Area= Perimeter

\(\pi(x/\sqrt{3}) ^2 = 3x\)
\(=> x = 9/\pi\)

From ...i)

Radius of the circumcircle =\(9/(\pi * \sqrt{3})\)
=\(3\sqrt{3}/\pi\)

Answer (B)