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Question
In the given figure, if PB || CF and DP || EF, then \[\frac{AD}{DE} =\]
Options
- \[\frac{3}{4}\]
- \[\frac{1}{3}\]
- \[\frac{1}{4}\]
- \[\frac{2}{3}\]
Solution
Given: PB||CF and DP||EF. AB = 2 cm and AC = 8 cm.
To find: AD: DE
According to BASIC PROPORTIONALITY THEOREM, if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
In ∆ACF, PB || CF.
`(AB)/(BC)=(AP)/(PF)`
`(AP)/(PF)=2/(8-2)`
`(AP)/(PF)=2/6`
`(AP)/(PF)=1/3........(1)`
Again, DP||EF.
`(AD)/(DE)=(AP)/(PF)`
`(AD)/(DE)=1/3`
Hence we got the result Option `b`.
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