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If, in a $△ A B C, (a + b + c) (b + c - a) = λ b c,$ then

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λ<0

λ>4

λ>0

0<λ<4

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Correct option is D

We have,(a+b+c)(b+c−a)=λbc⇒2s(2s−a)=λbc⇒s(s−a)bc=λ4⇒cos2⁡A2=λ4 ⇒0<λ4<1⇒0<λ<4⇒∵cos2⁡A2≤1 ∵cos2⁡A2≤1

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If, in a △ABC, (a+b+c)(b+c−a)=λbc, then

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Ready to Test Your Skills?

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If, in a $△ A B C, (a + b + c) (b + c - a) = λ b c,$ then