Question

In the given figure, AB = 16 cm, BC = 12 cm and CA = 6 cm; find the length of CD.

Answer 1

In right-angled triangle ΔACD, applying Pythagoras’ theorem gives:

AD² = AC² − CD² = 6² − CD² = 36 − CD²

In right-angled triangle ΔABD, applying Pythagoras’ theorem gives:

AD² = AB² − BD² = 16² − (BC + CD)² = 16² − (12 + CD)²

AD² = 256 − (144 + 24 × CD + CD²) = 112 − 24 × CD − CD²

Equating the two expressions for AD²:

36 − CD² = 112 − 24 × CD − CD²

Adding CD² to both sides and rearranging terms:

24 × CD = 112 − 36

24 × CD = 76

CD = `76/24 = 19/6` cm