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nishant kumar agarwal Grade: Upto college level

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

7 years ago

147 Points

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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Regards,

7 years ago
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