Question

In the following figure, ABCD to a trapezium with AB || DC. If AB = 9 cm, DC = 18 cm, CF = 13.5 cm, AP = 6 cm and BE = 15 cm, Calculate: AF

Answer 1

In ΔAPB and ΔFPD 

∠APB = ∠FPD  ...(Vertically opposite angles)

∠BAP = ∠DFP  ...(Since AB || DF)

ΔAPB ∼ ΔFPD  ...(AA criterion for similarity)

`=> (AP)/(FP) = (AB)/(FD)`

`=> 6/(FP) = 9/31.5`

`=>` FP = 21 cm

So AF = AP + PF

= 6 + 21

= 27 cm