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Question
ΔABC is right angled at A. AD is drawn perpendicular to BC. If AB = 8cm and AC = 6cm, calculate BD.
Solution
In ΔABC,
Using Pythagoras theorem
BC2 = AB2 + AC2
BC2 = 82 + 62
BC2 = 64 + 36
BC = `sqrt(100)` = 10..........(i)
In ΔABD,
Using Pythagoras theorem
AD2 = AB2 - BD2
AD2 = 82 - BD2......(ii)
In ΔACD,
Using Pythagoras theorem
AD2 = AC2 - CD2
AD2 = 62 - CD2......(iii)
Equaliting (ii) and (iii)
82 - BD2 = 62 - CD
∵ CD = BC - BD
82 - BD2 = 62 - (BC - BD)2
CD = BC - BD
BC = 10cm(from (i))
82 - BD2 = 62 - (10 - BD)2
82 - BD2 = 62 - (100 - 20BD + BD2)
64 + BD2 = 62 - (100 + 20BD - BD2)
64 = -64 + 20BD
20BD = 128
BD = 6.4cm.
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