Answer:
The radius of the incircle =12 cm
Step-by-step explanation:
Given problem is finding the radius of the in circle with sides of the triangle 32 cm, 60 cm 68 cm
Radius of incircle = area of the triangle÷semi perimeter of triangle
⇒ perimeter of the triangle (s) = [tex]\frac{32+60+68}{2}[/tex] = [tex]\frac{ 160}{2}[/tex] = 80 cm
⇒ area of the triangle = [tex]\sqrt{ s(s-a)(s-b)(s-c)}[/tex]
= [tex]\sqrt{80(80-32)(80-60)(80-68)}[/tex]
= [tex]\sqrt{80(48)(20)(12)}[/tex] [ 80 =8(5)(2), 48 = 8(2)(3)]
= [tex]\sqrt{ 8(5)(2)(8)(2)(3)(5)(4)(3)}[/tex] [ 20 =4(5), 12 = 4(3) ]
= [tex]\sqrt{ (8 ^{2})( 5 ^{2} )(4 ^{2})(3 ^{2} )(2^{2}) }[/tex]
= 8(5)(4)(3)(2) = 960 cm²
⇒ radius of the incircle = 960/ 80
= 12 cm