In given figure, ABC is triangle right angled at B and BD ⊥ AC. If AD = 4 cm and CD = 5 cm, then find BD and AB.

Question

Philoid · Accepted Answer

Given,

∆ABC in which ∠B = 90° and BD ⊥ AC

Also, AD = 4 cm and CD = 5 cm

In ∆ADB and ∆CDB,

∠ADB = ∠CDB [each equal 90°]

∠BAD = ∠DBC [each equal to 90°-∠C]

∴ ∆DBA ∼ ∆DCB [by AAA similarity criteria]

Then,

In right angled ∆BDC,

BC² = BD² + CD² [by Pythagoras theorem]

= BC² = (2√5)² + (5)²

= BC² = 20 + 25 = 45

= BC = √45 = 3√5

Again,

Hence, BD = 2√5cm and AB = 6cm.