Question

The radius of the circle inscribed in an equilateral triangle with side 6 cm is m root 3 cm then m equal to

Answer 1

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The height of an Equilateral triangle is 6√3cm Find its area. 10.2 K+ Views .... Each side of an equilateral triangle is equal to the radius of a circle whose area is 154 cm2.

Answer 2

Answer:

Step-by-step explanation:

Suppose you have a triangle ABC. Let AD be the median where D lies on BC. Since it is an equilateral triangle, D will be the mid-point of side BC.

Now, for the time being, let us assume that the length of each side of the equilateral triangle is x.

=> AD = x/2

Also we know that all the angles of an equilateral triangle measure 60 degrees. Using trigonometry, sin60 = AD/AB

=> sqrt(3)/2 = AD/AB

=> AD = AB * sqrt(3)/2

We also know that the centroid of an equilateral triangle divides the median in two parts in the ratio 2:1 and bigger part of that median is the centre of the circle.

So the bigger part of the median (or the radius of the circle is)

       2/3 * sqrt(3)/2 * AB

i.e., x/sqrt(3)   [AB=x]

i.e.,  6/sqrt(3)   [x=6, which is given]

=2*sqrt(3)