Drawn from origin are two mutually perpendicular lines forming an isosceles triangle together with the straight line 2x+y=a.  Then the area of this triangle is

Let the two perpendiculars through the intersect 2x+y=a  A and B so that the triangle OAB is isosceles. OM= length of perpendicular from O to AB, OM=a5 . Also AM=MB=OM                      ⇒AB=2a5.  Area of ΔOAB=12AB.OM            =12.2a5.a5=a25