Question:
In the given figure, if PB || CF and DP || EF, then ADDE=
(a) 34
(b) 13
(c) 14
(d) 23
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.
$\frac{\mathrm{AB}}{\mathrm{BC}}=\frac{\mathrm{AP}}{\mathrm{PF}}$
$\frac{\mathrm{AP}}{\mathrm{PF}}=\frac{2}{8-2}$
$\frac{\mathrm{AP}}{\mathrm{PF}}=\frac{2}{6}$
$\frac{\mathrm{AP}}{\mathrm{PF}}=\frac{1}{3}$.....(1)
Again, DP||EF.
$\frac{\mathrm{AD}}{\mathrm{DE}}=\frac{\mathrm{AP}}{\mathrm{PF}}$
$\frac{\mathrm{AD}}{\mathrm{DE}}=\frac{1}{3}$
Hence we got the result option $(b)$.