Question

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

Answer 1

It is given that ABC is a right angled triangle and BD is the altitude drawn from the right angle to the hypotenuse.
In Δ BDC and Δ ABC, we have :   

∠𝐴𝐵𝐶= ∠𝐵𝐵𝐶=90° (𝑔𝑖𝑣𝑒𝑛)
∠𝐶= ∠𝐶 (𝑐𝑜𝑚𝑚𝑜𝑛)  

By AA similarity theorem, we get :
Δ BDC- Δ ABC 

`(AB)/(BD)+(BC)/(DC)` 

⇒ `5.7/3.8=(BC)/5.4` 

⇒ BC=`5.7/3.8xx5.4` 

⇒8.1 

Hence, BC = 8.1 cm