in fig 4 144 we have AB||CD||EF if AB=6cm , CD=x cm, EF=10cm, BD=4cm and DE=y cm, calculate the values - Maths - Triangles

Question

in fig 4 144 we have AB||CD||EF if AB=6cm , CD=x cm, EF=10cm,
BD=4cm and DE=y cm, calculate the values of x and y

Shubhangi Pai · Answer

Consider ΔADB and ΔEDF,

∠ADB = ∠EDF (Vertical angles)
∠ABD = ∠FED (Alternate angles)
∠BAD = ∠EFD (Alternate angles)

∴ ΔADB ~ ΔEDF (ASA criterion)

⇒ BD/DE = AB/FE
⇒ 4/y = 6/10
⇒ 6y = 40
⇒ y = 40/6 = 20/3
⇒ y = 6 67

Similarly, ΔADE ~ ΔCDE (AA criterion)
⇒ DE/BE = DC/BA

⇒ 6 67 / 10 67 = x / 6

⇒ x = 6 x (6 67 / 10 67)

⇒ x = 3 75

hence, the values of x and y are 3 75 and 6 67

in fig.4.144 we have AB||CD||EF.if AB=6cm , CD=x cm, EF=10cm, BD=4cm and DE=y cm, calculate the values of x and y