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2014-11-12T15:48:32+05:30

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Let us say the equation of such a line is 
    x/a + y/b = 1,   here a and b are intercepts on the coordinate axis by the line.

 then 1/2*  a b = area of triangle = 8 sq units   => ab = 16 square units

3/a + 1/b = 1    => 3 b + a = ab = 16 
                   3 b + 16/b = 16
                     3 b² -16 b + 16 = 0
      
                     b = [ 16 +- √(256-192) ] / 6  =  4/3  or 4
           a = 12  or  4 

hence the two lines are :    bx + ay = ab  =>  
                     4/3 x + 12 y = 16  =>  x + 9 y = 12
                     4 x + 4 y   = 16       =>  x + y = 4


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