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Question
In the given figure, if AB || CD || FE then find x and AE.
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Solution 1
Construction: Join AF intersecting CD at X.
In ΔABF, DX || AB
`"FD"/"DB"="FX"/"XA"` ...(1) (By Basic proportionality theorem)
In ΔAEF, XC || FE
`"FX"/"XA"="EC"/"CA"` ... (2) (By Basic proportionality theorem)
From (1) and (2), we get
`"FD"/"DB"="EC"/"CA"`
`4/8 = x/12`
x = 6
Now, AE = AC + CE
= 12 + 6
= 18
Solution 2
line AB || line CD || line FE ...(given)
∴ `("BD")/("DF") = ("AC")/("CE")` ...(Property of three parallel lines and their transversals)
∴ `8/4 = 12/x`
∴ x = `(12 xx 4)/8`
∴ x = 6 units
Now, AE = AC + CE [A - C - E]
= 12 + x
= 12 + 6
= 18 units
∴ x = 6 units and AE = 18 units
Notes
Students can refer to the provided solutions based on their preferred marks.
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