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Question
In the following figure, XY is parallel to BC, AX = 9 cm, XB = 4.5 cm and BC = 18 cm.
Find : XY
Solution
In ΔAXY and ΔABC,
∠XAY = ∠BAC ...(Common angle)
∠AXY = ∠ABC ...(Corresponding angles for parallel lines, XY || BC)
∠AYX = ∠ACB ...(Corresponding angles for parallel lines, XY || BC)
Thus, ΔAXY ∼ ΔABC
Hence, `(AX)/(AB) = (XY)/(BC)` ...(Using similar triangle property)
`(AX)/(AX + XB) = (XY)/18`
`9/(9 + 4.5) = (XY)/18`
`XY = (18 xx 9)/(13.5)`
XY = 12 cm
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