Question

find the radius of the incircle of a triangle with sides measuring 32 CM 60 CM 68 CM​

Answer 1

Answer:

Step-by-step explanation:

radius of the incircle of triangle= area/semi perimeter

p is half the perimeter, or

P=(18+24+30)/2 = 36

A=square root of (36(36-18)(36-24)(36-30))

=square root of (36*18*12*6)

=216 s.cm

radius of the incircle of triangle= 216/36=6cm

Answer 2

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) =  $\frac{32+60+68}{2}$ =  $\frac{ 160}{2}$ = 80 cm

⇒ area of the triangle = $\sqrt{ s(s-a)(s-b)(s-c)}$  

                   =  $\sqrt{80(80-32)(80-60)(80-68)}$

                   = $\sqrt{80(48)(20)(12)}$                 [ 80 =8(5)(2), 48 = 8(2)(3)]

                   =  $\sqrt{ 8(5)(2)(8)(2)(3)(5)(4)(3)}$    [ 20 =4(5), 12 = 4(3) ]

                   = $\sqrt{ (8 ^{2})( 5 ^{2} )(4 ^{2})(3 ^{2} )(2^{2}) }$  

                   = 8(5)(4)(3)(2) = 960 cm²

⇒ radius of the incircle = 960/ 80

                                      = 12 cm