Question

Q.7) Seg AM is a median of triangle ABC.
If AM = 9 and AB2+ AC2 = 290 then find
BC.
16
18
20
24
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Answer 1

Question:-

Seg AM is a median of triangle ABC. If AM = 9 and AB²+ AC² = 290 then find

BC.

Formula Used:-

Apollonius Theorem, which states that AB² + AC² = 2(AM² + BM²), where AM is the median

Answer:-

Refer to the attachment

Applying Apollonius theorem,

AB² + AC² = 2(AM² + BM²)

Given AB² + AC² = 290 and AM = 9. So putting the values,

➞ 290 = 2 * (9² + BM²)

➞ 290/2 = 9² + BM²

➞ 145 = 81 + BM²

➞ BM² = 64

➞ BM = 8

As AM is median, BM = MC. So BC = 2BM

➞ BC = 2 * BM

➞ BC = 2 * 8

➞ BC = 16

Ans. BC = 16