What is the radius of the circle inscribed in triangle $abc$ if $ab = 12, ac=14, bc=16$? express your answer in simplest radical form?

The triangle given above is a scalene triangle as non of its given sides are equal. To determine the area of the triangle, we use the Heron's formula which is expressed as below,
    A = sqrt ((s)(s - a)(s - b)(s - c))

where a, b, and c are the lengths of the sides and s is the semiperimeter ((a+b+c)/2)

The area of the triangle can also be computed through the equation, A = rs
where r is the radius of the inscribed circle. Equating both areas,
     A = sqrt ((s)(s-a)(s-b)(s-c)) = rs
Divide the equation by s,
      r = sqrt ((s)(s-a)(s-b)(s-c)) / s

Solving for s,
    s = (12+14+16)/2 = 21

Substituting to the equation for r,
    r = sqrt ((21)(21-12)(21-14)(21-16)) 21
    r = sqrt 15
    r = 3.87

ANSWER: r = 3.87

a - base

b - exponent

so,

the base is 8the exponent is 3the exponent tells you to multiply 8 together three timesthe expanded form is 8*8*8