what is the value of x Will make DE parallel AB in given figure
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Step-by-step explanation:
Given :
In ∆ABC , DE//AB
AD = 8x + 9 , CD = x + 3 ,
BE = 3x + 4 , CE = x ;
Solution :
In ∆ABC , DE // BC
CD/DA = CE/BE
[ Thales theorem ]
( x + 3 )/( 8x + 9 ) = x/( 3x + 4 )
=> ( x+3 )( 3x+4 ) = x( 8x+9 )
=> 3x² + 4x + 9x + 12 = 8x² + 9x
=> 3x² + 13x + 12 = 8x² + 9x
=> 5x² - 4x - 12 = 0
=> 5x² - 10x + 6x - 12 = 0
=> 5x( x - 2 ) + 6 ( x - 2 ) = 0
=> ( x - 2 )( 5x + 6 ) = 0
x - 2 = 0 or 5x + 6 = 0
Therefore ,
x = 2 or x = -6/5
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