Question

In fig, ad⊥bc , ab=25 ad=17cm find bd,dc,bc

Answer 1

Given :

• In ΔABC :
• ∠ADC = ∠ABC = 90°
• AD ⊥ BC
• AB = 25cm
• AD = 17cm
• AD = 15cm

To find

• Length of :
• BD
• DC
• BC

Solution :

• In ΔADB :
• ∠ADB = 90°
• BD² = AB² - AD²  (Pythagoras Theorem)
• BD² = 25² - 15²
• BD² = 625 - 225
• BD² = 400
• BD = √400
• BD = 20

☯ Length of BD = 20cm

• In ΔADC :
• ∠ADC = 90°
• DC² = AC² - AD²   (Pythagoras Theorem)
• DC² = 17² - 15²
• DC² = 289 - 225
• DC² = 64
• DC = √64
• DC = 8

☯ Length of DC = 8cm

• BC = BD + DC
• As BD and DC together make up BC
• BC = 20 + 8
• BC = 28

☯ Length of BC = 28cm