In the given figure, ∠ABC = 90° and BD⊥AC. If AB = 5.7cm, BD = 3

1.	In the given figure, ∠ABC = 90° and BD⊥AC. If AB = 5.7cm, BD = 3.8cm and CD = 5.4cm, find BC.
Answer» It is given that ABC is a right angled triangle and BD is the altitude drawn from the right angle to the hypotenuse. In ∆ BDC and ∆ ABC, we have : ∠ABC = ∠BBC = 90° (given) ∠C = ∠C (common) By AA similarity theorem, we get : ∆ BDC- ∆ ABC AB/BD = BC/DC ⇒ 5.7/3.8 = BC/5.4 ⇒ = 5.7/3.8 ×5.4 = 8.1 Hence, BC = 8.1 cm

In the given figure, ∠ABC = 90° and BD⊥AC. If AB = 5.7cm, BD = 3.8cm and CD = 5.4cm, find BC.

Answer»

It is given that ABC is a right angled triangle and BD is the altitude drawn from the right angle to the hypotenuse.

In ∆ BDC and ∆ ABC, we have :

∠ABC = ∠BBC = 90° (given)

∠C = ∠C (common)

By AA similarity theorem, we get :

∆ BDC- ∆ ABC

AB/BD = BC/DC

⇒ 5.7/3.8 = BC/5.4

⇒ = 5.7/3.8 ×5.4

= 8.1

Hence, BC = 8.1 cm