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Question

In the given figure, AX:XB=3:5 and XY||BC.

If  XY = 18 cm, then BC = ___ .



A

36 cm

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B

40 cm

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C

44 cm

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D

48 cm

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Solution

The correct option is C

44 cm


We are given that in the ΔABC,AX:XB=3:5 and XY||BC.

XBAX=53

XBAX+1=53+1

XB+AXAX=5+33

ABAX=83

AXAB=38

Now in ΔAXYand ΔABC,

AXY=ABC (Corresponding angles)

XAY=BAC(Common in both triangles)

ΔAXYΔABC(By AA similarity criterion)

AXAB=XYBC

38=18BC

BC=18×83 = 48 cm


Mathematics

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