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CBSE Class 10 Answered

given ; A and B trisect the side EF of  RIGHT triangle DEF prove that 8 D B squared space equals space 3 D F squared space plus space 5 D A squared. Angle DEF=90 degrees and E-A-B-F of side EF .
Asked by apurva151 | 16 Feb, 2016, 04:57: PM
answered-by-expert Expert Answer
 
begin mathsize 14px style S i n c e space A thin space a n d space B space a r e space t h e space p o i n t s space o f space t r i s e c t i o n space o f space E F comma space w e space h a v e space E A equals A B equals B F L e t space E A equals A B equals B F space equals space m T h e n comma space E B equals 2 m space a n d space E F equals 3 m I n space r i g h t space t r i a n g l e space D E A comma D A squared equals D E squared plus E A squared space space space space space space space rightwards double arrow D A squared equals D E squared plus x squared space space space space space space..... left parenthesis 1 right parenthesis I n space r i g h t space t r i a n g l e space D E B comma space D B squared equals D E squared plus E B squared space space space space rightwards double arrow D B squared equals D E squared plus 4 x squared space space space space.... left parenthesis 2 right parenthesis I n space r i g h t space t r i a n g l e space D E F comma D F squared equals D E squared plus E F squared space space space space rightwards double arrow D F squared equals D E squared plus 9 x squared space space space space space.... left parenthesis 3 right parenthesis N o w comma space 8 D B squared minus 3 D F squared minus 5 D A squared equals 8 left parenthesis D E squared plus 4 x squared right parenthesis minus 3 left parenthesis D E squared plus 9 x squared right parenthesis minus 5 left parenthesis D E squared plus x squared right parenthesis rightwards double arrow 8 D B squared minus 3 D F squared minus 5 D A squared equals 0 rightwards double arrow 8 D B squared equals 3 D F squared plus 5 D A squared end style
Answered by Rashmi Khot | 16 Feb, 2016, 06:06: PM

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