In the figure given below, AB||EF||CD, If AB =22.5 cm, EP =7.5 cm, PC =15 cm and DC =27 cm.
Calculate: (i) EF (ii) AC
EF = 13.5 cm, AC = 37.5 cm
In the given figure.
AB||EF||CD
AB =22.5 cm, EP=7.5 cm
PC =15 cm and DC =27 cm
To calculate: (i) EF (ii)AC
In ΔDCP and ΔPEF
∠CPD=∠EPF (Vertically opp. angles)
∠DCP=∠PEF (Alternate angles)
∴ΔDCP∼ΔPEF (AA axiom)
∴DCEF=CPPE⇒27EF=157.5
⇒EF=27×7.515=272=13.5cm
Similarly in ΔABC,EF||AB
∴ΔCDF∼ΔACB
∴CEAC=EFAB
22.5AC=13.522.5
AC=22.5×22.513.5
=225×225135×10×10=37510cm
∴AC=37.5cm