KVPY 2019 SA Exam Previous Papers

Question : 6 of 80

Marks: +1, -0

The sides

a, b, c

of a triangle satisfy the relations

c^{2}

=2 a b

and

a^{2}+c^{2}=3 b^{2}

. Then the measure of

∠ B A C

, in degrees, is

Solution:

c^{2}=2 a b \;\;\;\;\;⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(i)

a^{2}+c^{2}=3 b^{2} \;\;\;\;\;⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(ii)

Substitute (i) in (ii) equation,
we get,

a^{2}+2 a b=3 b^{2}

⇒(a+b)^{2}+4 b^{2}

⇒ a=b, c=√{2} a

⇒ ∠ A=45^{∘}=∠ B

and

∠ C=90^{∘}

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