Question

in figure xy parallel AC and XY divided tringular region ABC into two parts equal in areas. determine AX/AB​

Answer 1

Step-by-step explanation:

Ar. AXYC = Ar. BXY

Ar. AXYC +Ar. BXY =2 Ar. BXY

Ar.ABC =2 Ar. BXY

Hence, Ar.BXYAr.ABC=2 ...(I)

In △s ABC and BXY,

∠XBY=∠ABC (Common angle)

∠BXY=∠BAC (Corresponding angles of parallel lines XY and AC)

∠BYX=∠BCA (Corresponding angles of parallel lines XY and AC)

△ABC∼△XBY (AAA postulate)

Now, Ar.BXYAr.ABC=BX2AB2 (Similar triangle Property)

2=BX2AB2

BXAB=2

AB=2BX

AX+XB=2XB

AX=(2−1)XB

AX:XB=(2−1):1