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Question Number 113092 by bobhans last updated on 11/Sep/20
What is the area of a tringle where the  sides of triangle are 91 cm, 98 cm, and 105 cm
Whatistheareaofatringlewherethesidesoftriangleare91cm,98cm,and105cm
Answered by bemath last updated on 11/Sep/20
question. What is the area of  triangle where the sides of triangle  are 91 cm, 98 cm and 105 cm?  area = ((√(4a^2 b^2 −(a^2 +b^2 −c^2 )^2 ))/4)  where a,b,c are the length sides of △.  hence area = ((√(4×91^2 ×98^2 −(91^2 +98^2 −105^2 )^2 ))/4)                          = 4116 cm^2
question.Whatistheareaoftrianglewherethesidesoftriangleare91cm,98cmand105cm?area=4a2b2(a2+b2c2)24wherea,b,carethelengthsidesof.hencearea=4×912×982(912+9821052)24=4116cm2
Commented by bobhans last updated on 11/Sep/20
waw....the new formula
waw.thenewformula
Commented by MJS_new last updated on 11/Sep/20
the formula is not new, it′s Heron′s Formula  usually we write it  Area=((√((a+b+c)(a+b−c)(a+c−b)(b+c−a)))/4)
theformulaisnotnew,itsHeronsFormulausuallywewriteitArea=(a+b+c)(a+bc)(a+cb)(b+ca)4
Commented by bobhans last updated on 11/Sep/20
Archimedes Theorem  16(area)^2 =4a^2 b^2 −(c^2 −a^2 −b^2 )^2   area = (√((4a^2 b^2 −(c^2 −a^2 −b^2 )^2 )/(16)))
ArchimedesTheorem16(area)2=4a2b2(c2a2b2)2area=4a2b2(c2a2b2)216
Commented by bemath last updated on 11/Sep/20
not same sir. i think it from   Archimedes theorem.  sorry if i wrong. hahaha
notsamesir.ithinkitfromArchimedestheorem.sorryifiwrong.hahaha
Commented by MJS_new last updated on 11/Sep/20
(a+b+c)(a+b−c))a+c−b)(b+c−a)=  =−(a^4 +b^4 +c^4 )+2(a^2 b^2 +a^2 c^2 +b^2 c^2 )=  4a^2 b^2 −(a^2 +b^2 −c^2 )^2 =  =4a^2 b^2 −(a^4 +b^4 +c^4 +2(a^2 b^2 −a^2 c^2 −b^2 c^2 ))=  =−(a^4 +b^4 +c^4 )+2(a^2 b^2 +a^2 c^2 +b^2 c^2 )
(a+b+c)(a+bc))a+cb)(b+ca)==(a4+b4+c4)+2(a2b2+a2c2+b2c2)=4a2b2(a2+b2c2)2==4a2b2(a4+b4+c4+2(a2b2a2c2b2c2))==(a4+b4+c4)+2(a2b2+a2c2+b2c2)
Answered by malwaan last updated on 11/Sep/20
((91+98+105)/2) = ((294)/2) = 147  so the area =  (√(147(147−91)(147−98)(147−105)))  = (√(147×56×49×42))  = (√(16941456)) = 4116
91+98+1052=2942=147sothearea=147(14791)(14798)(147105)=147×56×49×42=16941456=4116
Commented by bemath last updated on 11/Sep/20
same sir with my answer.  please check
samesirwithmyanswer.pleasecheck
Commented by malwaan last updated on 11/Sep/20
yes  and thanks for this new formula
yesandthanksforthisnewformula

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