Question

the line segment XYlltoAC of triABC and it divides the tri into two parts of equal areas. Prove that AX/AB=root2-1/root2

Answer 1

we have XYllAC [GIVEN]

So <BXY=<A AND <BYX=<C [CORRESPONDING ANGLES]

THERE FORE TIANGLE ABC SIMILAR TRIANGLE XBY

SO ar[ABC]byar[XBY]=AB BY XB WHOLE SQUAR

ALSO ar[ABC]=2ar[XBY]

SO ar[ABC] BY ar[XBY]=2by1

AB byXB squar=2 by 1 i;e AB by XB=root 2 by 1

or XB by AB=1 by root 2

or AB-XB by AB=root2-1 by root 2  i;eAX by AB=root2-1 by root 2=2-root2 by 2