A triangle has sides with lengths of 5, 7, and 4. What is the radius of the triangles inscribed circle?

Question

2414 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-24T07:45:36

#Radius# #o##f# #cir##cl##e#=#sqrt6/2#

#Radius# #o##f# #cir##cl##e# #i##nscribed# #i##nside# #a# #triangle#=#(Area# #o##f# #triangle)##/##s#
#Where# #s=semi# #perimeter# #o##f# #triangle#

#s=(5+7+4)/2=16/2=8#

#a=5,b=7,c=4#

#Area# #o##f# #triangle#=#sqrt[s(s-a)(s-b)(s-c)]#

#rarr=sqrt[8(8-5)(8-7)(8-4)]#

#rarr=sqrt[8(3)(1)(4)]#

#rarr=sqrt[8(96)]#

#rarr=sqrt96#

#So,Radius# #o##f# #cir##cl##e##=sqrt96/8=(2sqrt24)/8=sqrt24/4=(2sqrt6)/4=sqrt6/2#