Question

ΔABC is right angled at A. AD is drawn perpendicular to BC. If AB = 8cm and AC = 6cm, calculate BD.

Answer 1

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.