Question

ABC is a right-angled triangle with <ACB = 90°, BC = 12 cm, AB = 15 cm and
CD = 5 cm. Find the lengths of BD and AD.

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Answer 1

Answer:

AD =4

Step-by-step explanation:

In Triangle BDC

BD²= BC²+CD²

BD² = 12² + 5²

BD² = 144 +25

BD² = 169

BD = 13cm

In Triangle ABC

AB²= AC² + BC²

15² = AC² + 12²

225 = AC² + 144

AC² = 225 - 144

AC² = 81

AC = 9

so,AC = AD + CD

9 = AD + 5

AD = 9-5

AD = 4

Hence,

BD = 13 cm ;

AD=4cm

Answer 2

Answer:

BD = 10.9 cm and AD = 4.1 cm

Step-by-step explanation:

(To solve this problem, first draw a rough figure)

By Pythagoras Theorem in ΔBCD,

CD² + BD² = BC²

25 + BD² = 144

BD² = 119 ⇒ BD = √119 ≈ 10.9 cm

BD + AD = AB

10.9 + AD = 15 ⇒ AD = 4.1 cm

Hence solved