In ΔABD, C is the midpoint of BD. If AB = 10cm, AD = 12cm & AC = 9cm, then BD = ?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 2√41 cm
As we know:
AB2 + AD2 = 2(BC2 + AC2)
⇒ 102 + 122 = 2(BC2 + 92)
⇒ 100 + 144 = 2(BC2 + 81)
⇒ 2BC2 = 244 - 162
⇒ 2BC2 = 82
⇒ BC2 = 41
⇒ BC = √41
Hence,
BD = 2BC = 2√41 cm