KVPY 2020-21 SB SX Exam Previous Papers

Question : 90 of 120

Marks: +1, -0

Let a = BC, b = CA, c = AB be the side lengths of a triangle ABC, and m be the length of the median through A. If a = 8, b – c = 2, m = 6, then the nearest integer to b is

Validate

Solution:

{m}^{2}={2 {b}^{2}+2 {c}^{2}-{a}^{2}}/{4}

\⇒144+64=2[{b}^{2}+({b}-2)^{2}]

\⇒ 104=2 {b}^{2}-4 {b}+4

\⇒{b}^{2}-2 {b}-50=0

\⇒({b}-1)^{2}=51

\⇒{b}=1+\√{51} \∈(8,9)

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