Question

1. In ∆ ABC, AD is a median. If AB = 8, AC = 15
and AD = 8.5, find BC.​

Answer 1

Given :-

• AD is a median.
• AB = 8
• AC = 15
• AD = 8.5.

To Find :-

• BC ?

Solution :-

Since AD is a median . using Apolloniu's Theorem we get,

→ AB² + AC² = 2(AD² + BD²)

Putting all values we get,

→ 8² + 15² = 2(8.5² + BD²)

→ 64 + 225 = 2(72.25 + BD²)

→ 289 = 144.5 + 2BD²

→ 2BD² = 289 - 144.5

→ 2BD² = 144.5

→ BD² = 72.25

→ BD² = (8.5)²

Square - root both sides,

→ BD = 8.5

Therefore,

→ BD = DC = 8.5 (AD is median.)

Hence,

→ BC = 8.5 * 2 = 17 . (Ans.)

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Answer 2

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