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CBSE Class 10 Answered

In right angled Triangle ABC if D and E trisect BC then prove that 8 AE2 = 3 AC2 + 5 AD2         
Asked by gpnkumar0 | 04 Mar, 2018, 08:37: PM
answered-by-expert Expert Answer
 
begin mathsize 16px style SInce space straight D space and space straight E space trisects space BC comma
BD equals DE equals EC
Let space BD equals DE equals EC equals straight x
Then comma space BE equals 2 straight x space and space BC equals 3 straight x
In space triangle ABD comma
AD squared equals AB squared plus BD squared
rightwards double arrow AD squared equals AB squared plus straight x squared space space space space space space.... left parenthesis straight i right parenthesis
In space triangle ABE comma
AE squared equals AB squared plus BE squared
rightwards double arrow AE squared equals AB squared plus 4 straight x squared space space space space space space.... left parenthesis ii right parenthesis
In space triangle ABC comma
AC squared equals AB squared plus BC squared
rightwards double arrow AC squared equals AB squared plus 9 straight x squared space space space space space space.... left parenthesis iii right parenthesis
Now comma space 8 AE squared minus 3 AC squared minus 5 AD squared
equals 8 left parenthesis AB squared plus 4 straight x squared right parenthesis minus 3 left parenthesis AB squared plus 9 straight x squared right parenthesis minus 5 left parenthesis AB squared plus straight x squared right parenthesis
equals 8 AB squared plus 32 straight x squared minus 3 AB squared minus 27 straight x squared minus 5 AB squared minus 5 straight x squared
equals 0
rightwards double arrow 8 AE squared equals 3 AC squared plus 5 AD squared end style
Answered by Rashmi Khot | 05 Mar, 2018, 09:50: AM
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