Let a = B C , b = C A , c = A B be the side lengths of a triangle A B C , 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

Question

Let a = B C , b = C A , c = A B be the side lengths of a triangle A B C , 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, 7, 8, 9, 10

MARKS App · Accepted Answer

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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