Determine the circle radius if the circle is inscribed in a triangle wich has the sides lenghts of 13, 14, and 15 .

Expert Answers

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Let A be the area of the triangle

P be the perimeter of the tirangle

and r is the radius of the circlr:

Then, we know that:

   A = r * P/2

Let us caclculateL

P = 13 + 14 + 15 = 42

==> p/2 = 42/2 = 21

Now for A:

A =sqrt[ p/2 (p/2- 13)(p/2 - 14)(p/2 - 15)]

     = sqrt[21*8*7*6]

     = 84

Then:

 A = r* p/2

84 = r * 21

==> r= 84/21= 4

Then the radius = 4 units

 

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