1.

Observe the right triangle ABC, right angled at B, where AP = x units , PC = (x + 5 ) units and AB = 5 units as shown below . Find the length of PC :

Answer»

In ∆APB, ∠APB = 180 - 90 = 90° (Linear pair) 

So AP2 + BP2 = AB2

⇒ x2 +   BP2 = 25

∴ BP = √(25 - x2) 

In ∆APB and ∆ABC

∠A = ∠A (Common)

∠ APB = ∠ABC (90° each)

 ∴ ∆APB ∼ ∆ABC (AA similarity) - (1)

Similarly, ∆BPC ∼ ∆ABC (AA similarity) - (2)

From (1) and (2) 

 ∆APB ∼ ∆BPC 

⇒ AP/BP = BP/PC

 ⇒ BP2 = AP × PC

⇒ 25 - x2 = x(5 + x)

⇒ (5 + x)(5 - x) = x(5 + x)

⇒ 5 - x = x

∴ 2x = 5

x = 2.5. 

PC = x + 5 = 7.5 units


Discussion

No Comment Found

Related InterviewSolutions