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Question

In the given figure, the line segment XY is parallel in AC of ΔABC and is divided the triangle into two parts of equal areas then AXAB=212
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A
True
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B
False
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Solution

The correct option is A True
In ABC,XYAC

Area of ABC=2×AreaofBXY ........(1)

XYAC and BA is transversal.

BXY=BAC .......(2)

XBY=ABC(Common angle)

BXYBXY

AreaofBACAreaofBXY=2

BA2BX2=2

BABX=2

BA=2BX

BA=2(ABAX)

(12)BA=2AX

AXAB=122=212

Hence the given statement is true.

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