Question

In the following figure, AB, CD and EF are parallel lines. AB = 6cm, CD = y cm, EF = 10 cm, AC = 4 cm and CF = x cm. Calculate x and y 

Answer 1

In ΔFDC and ΔFBA,

∠FDC = ∠FDA (Corresponding angles)

∠DFC = ∠BFA (Common)

ΔFDC ~ ΔFBA (AA similarity)

`(CD)/(AB)=(FC)/(FA)`

`(Y)/(6)=(X)/(X+4)...............................(1)`

In ΔFCE and ΔACB,

∠FCE = ∠ACB (vertically opposite angles)

∠CFE = ∠CAB (Alternate angles)

ΔFCE ~ ΔACB (AA similarity)

`(FC)/(AC)=(EF)/(AB)`

`(X)/(4)=(10)/(6)⇒X=20/3=6-2/3 cm`

From (1):

`y=(6 xx 20/3)/(20/3+4)=3.75`