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Question

The line segment XY is parallel to side AC of Δ ABC and it divides the triangle into two parts of equal areas. Find the ratio BXAB.

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A
12
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B
12
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C
41
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D
21
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Solution

The correct option is A 12

Given: XY || AC
Ar(ABC)=2Ar(XBY)

Here, BXY = A and BYX = C (Corresponding angles)

ABC XBY (AA similarity criterion)

Ar(ABC)Ar(XBY)=(ABXB)2

Ar(ABC)=2Ar(XBY)

Ar(ABC)Ar(XBY)=21

(ABXB)2= 21
ABXB = 21

XBAB=12

Rationalising the denominator we get,

XBAB=22


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