1) In the given figure, XY || AC and XY divides the
triangular region ABC into two equal areas.
Determine AX; AB.
Answers
Answered by
2
Answer:
Correct option is
B
(
2
−1):1
Ar. AXYC = Ar. BXY
Ar. AXYC +Ar. BXY =2 Ar. BXY
Ar.ABC =2 Ar. BXY
Hence,
Ar.BXY
Ar.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.BXY
Ar.ABC
=
BX
2
AB
2
(Similar triangle Property)
2=
BX
2
AB
2
BX
AB
=
2
AB=
2
BX
AX+XB=
2
XB
AX=(
2
−1)XB
AX:XB=(
2
−1):1
do it this type
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