MathematicsIs it true that 1 p 2 = 1 a 2 + 1 b 2  , if ΔABC   is a right triangle in which ∠C= 90 °   CD⊥AB   and BC=a,CA=b,AB=c   and CD=p  ?

Is it true that 1 p 2 = 1 a 2 + 1 b 2  , if ΔABC   is a right triangle in which ∠C= 90 °   CD⊥AB   and BC=a,CA=b,AB=c   and CD=p  ?


  1. A
    True
  2. B
    False 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    We are given that ∠C= 90 ° ,CD⊥AB,BC=a,CA=b,AB=c,CD=p   and we have to check if  1 p 2 = 1 a 2 + 1 b 2  is true or not.
    The area of a triangle is 1 2 ×base×height  .
    First, we will find the area ΔABC   with base AB,
    ⇒ΔABC= 1 2 AB×CD ⇒ 1 2 ×c×p ⇒ 1 2 cp  
    The area of ΔABC   where BC is the base,
    ⇒ΔABC= 1 2 BC×AC ⇒ 1 2 ×a×b ⇒ 1 2 ab    Thus,
    ⇒ 1 2 cp= 1 2 ab ⇒cp=ab  
    Now,
    ⇒cp=ab ⇒ 1 p = c ab ⇒ 1 p 2 = c 2 a 2 b 2   As, c 2 = a 2 + b 2   so,
    ⇒ 1 p 2 = c 2 a 2 b 2 ⇒ 1 p 2 = a 2 + b 2 a 2 b 2 ⇒ 1 p 2 = 1 b 2 + 1 a 2  
    Hence, from the result the given statement is true and option 1 is correct.
     
    Chat on WhatsApp Call Infinity Learn