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CBSE Class 10 Answered

In a triangle ABC. AD is perpendicular to BC and 2BD = 3CD. Prove that 5AB^2 = 5AC^2+BC^2  
Asked by sudhanshukkeshri | 16 Feb, 2018, 06:31: PM
answered-by-expert Expert Answer
begin mathsize 16px style Given colon space In space increment ABC comma space AD perpendicular BC space and space 2 DB equals 3 CD To space prove colon space 5 AB squared equals 5 AC squared plus BC squared Proof colon 2 DB equals 3 CD DB over CD equals 3 over 2 DB equals 3 over 5 BC CD equals 2 over 5 BC Using space Pythagoras space in space increment ABD space and space increment ACD We space get space 25 AB squared equals 25 AD squared plus 9 BC squared......... left parenthesis straight i right parenthesis and 25 AC squared equals 25 AD squared plus 4 BC squared.............. left parenthesis ii right parenthesis From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis subtract space left parenthesis ii right parenthesis space from space left parenthesis straight i right parenthesis we space get space 25 AB squared minus 25 AC squared equals 25 AD squared plus 9 BC squared minus 25 AD squared minus 4 BC squared Simplifying space we space get 5 AB squared equals 5 AC squared plus BC squared end style
Answered by Sneha shidid | 16 Feb, 2018, 06:50: PM

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