Question

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 :

1. EF
2. AC

Answer 1

In the given figure,

AB || EF || CD

AB = 22.5 cm, EP = 7.5 cm

PC = 15 cm and DC = 27 cm

To calculate:

1. EF
2. AC

In ΔDCP and ΔPEF

∠CPD = ∠EPF   ...(Vertically opposite angles)

∠DCP = ∠PEF   ...(Alternate angles)

∴ ΔDCP ∼ ΔPEF  ...(AA axiom)

∴ `(DC)/(EF) = (CP)/(PE)`

`\implies 27/(EF) = 15/7.5`

`\implies EF = (27 xx 7.5)/15`

= `27/2`

= 13.5 cm

Similarly in ΔABC, EF || AB

∴ ΔCEF ∼ ΔACB

∴ `(CE)/(AC) = (EF)/(AB)`

`22.5/(AC) = 13.5/22.5`

`AC = (22.5 xx 22.5)/13.5`

= `(225 xx 225)/(135 xx 10 xx 10)`

= `375/10`

= 37.5 cm

Thus AC = 37.5 cm