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

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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#