Question 1204108
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Find the radius of the circle inscribed in an equilateral triangle whose perimeter is 10.8 units.
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<pre>
For any triangle, from consideration its area, it is easy to deduce the formula 
for the radius "r" of the inscibed circle

    {{{(1/2)*r*P)}}} = area.    (1)

where P is its perimeter.


For the given equilateral triagle,  P = 3a,  area = {{{a^2*(sqrt(3)/4)}}},  where "a" is the side length,

a = {{{10.8/3}}} = 3.6 units.


Therefore,  from (1)

    {{{(3/2)*r*a}}} = {{{a^2*(sqrt(3)/4)}}}.


It implies  r = {{{(a^2*(sqrt(3)/4))/((3/2)*a)}}} = {{{a*(sqrt(3)/6)}}} = {{{3.6*(sqrt(3)/6)}}} = {{{0.6*sqrt(3)}}} = 1.03923  (rounded).


<U>ANSWER</U>.  The radius of the inscribed circle is  r = {{{a*(sqrt(3)/6)}}} = {{{0.6*sqrt(3)}}} = 1.03923  (rounded).
</pre>

Solved.


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For deducing formula &nbsp;(1), &nbsp;see the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Proof-of-the-formula-for-the-area-of-a-triangle-via-the-radius-of-the-inscribed-circle.lesson>Proof of the formula for the area of a triangle via the radius of the inscribed circle</A> 

in this site.