Question

In fig.7.144,we have AB||CD||EF.If AB=6cm,CD=x cm,EF=10cm,BD=4cm and DE=y cm,calculate the value of x and y.​

Answer 1

Answer:

consider triangle ADB and triangle EDF

angle ADB=angle EDF (vertical angles)

angle ABD=angle FED(alternate angles)

angle BAD=angle EFD(alternate angles)

therefore, triangle ADB=triangle EDF(by AA similarity)

BD/DE=AB/FE

4/y=6/10

y=40/6=20/3

y=6.67cm

similarly, triangle ADE is similar to triangle CDE

DE/BE=DC/AB

6.67/10.67=x/6

x=6×6.67/10.67

x=3.75cm