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Question
In a right-angled triangle ABC,ABC = 90°, AC = 10 cm, BC = 6 cm and BC produced to D such CD = 9 cm. Find the length of AD.
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Solution
In ΔABC, ∠B = 90°
∴ AC2 = AB2 + BC2 ....(Pythagoras Theorem)
⇒ 102 = AB2 + 62
⇒ AB2 = 102 - 62
= 100 - 36
= 64
Now,
BD = BC + CD
= 6 + 9
= 15cm
⇒ BD2 = 225
In ΔABD, ∠B = 90°
∴ AD2 = AB2 + BD2
⇒ AD2 = 64 + 225 = 289
⇒ AD = 17cm.
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