Calculate the radius of the circle that is inscribed in triangle ABC whose sides are 3,4,5.

We notice that if we'll add the squares of the lengths
of 2 sides of the triangle ABC, we'll get the square of the biggest
one.

5^2 = 3^2 + 4^2

 25 = 9 +
16

25 = 25

This equality
certifies the fact that the triangle ABC is a right angled triangle, whose right angle
is A = 90 degrees.

The opposite side to the right angle A
is called hypothenuse, BC.

The hypothenuse represents the
diameter of the circle and we'll get:

R =
hypotenuse/2

Since hypotenuse is the biggest side of a
right angle triangle, that means that BC = 5.

R =
5/2

The radius of the inscribed circle in the given
triangle is:

r = S/p

S =
AB*AC/2

S = 3*4/2

S = 6 square
units (area of the triangle ABC)

p =
(3+4+5)/2

p = 12/2

p = 6
units

r = 6 square units/ 6
units

r = 1
unit.

The radius of the
inscribed circle is r = 1 unit.