Question

In the given figure, if PB || CF and DP || EF, then \[\frac{AD}{DE} =\]

Options

• \[\frac{3}{4}\]
• \[\frac{1}{3}\]
• \[\frac{1}{4}\]
• \[\frac{2}{3}\]

Answer 1

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`.