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.

Answer 1

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.