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Answer:
DC = 4 cm
Step-by-step explanation:
(i) In right angled ∆ABC
AB = 3 cm, BC = 12 cm
According to Pythagoras Theorem,
(AC)2 = (AB)2 + (BC)2
(AC)2 = (3)2 + (12)2
(AC) = √ 9 + 144
(AC) = √153 cm
(ii) In right angled triangle ACD
AD = 13 cm, AC = √153
According to Pythagoras Theorem,
DC2 = AB2 - AC2
DC2 = 169 - 153
DC = √16 = 4 cm
∴ Length of DC is 4 cm
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