Question

In the figure given above ; AB , CD and PQ are parallel. CD=3cm and AB=4cm. Find the length of PQ.​

Answer 1

Answer:

In △BCD and △BEF,

∠DBC=∠FBE (Common angle)

∠BCD=∠BEF (Corresponding angles of parallel lines CD and EF)

∠BDC=∠BFE (Corresponding angles of parallel lines CD and EF)

Thus, △BCD∼△BEF (AAA rule)

Hence, BEBC=BFBD=EFCD (Corresponding sides)

x+3x=BFBD=4.5y ..(I)

Similarly, △FCD∼△FAB

Thus, FAFC=ABCD=FBFD

7.5y=BFDF (II)

From I and II,

BD=4.5yBF and DF=7.5yBF

BD+DF=BF

4.5yBF+7.5