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in a triangle ABC, (a+b+c)(b+c-a)=Λbc if......(condition)?

in a triangle ABC, (a+b+c)(b+c-a)=Λbc if......(condition)?

Grade:Upto college level

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

Dear nishant

(a+b+c)(b+c-a)=abc

((b+c)+a)((b+c)-a)=abc

 (b+c)2 -a2 =abc

 b2 +c2 +2bc -a2 =abc

b2 +c2  -a2 =abc -2bc

(b2 +c2  -a2)/2bc =a/2 - 1

 cosA =a/2 - 1

 since  -1< cosA <1

  so          -1< a/2 - 1 <1

                0< a/2<2

                0<a<4

 

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2 years ago
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