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 : AC

 

Answer 1

In ΔPCD and ΔPEF,

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

∠DCE = ∠FEP ...(since DC || EF)

ΔPCD ∼ ΔPEF ...(AA criterion for similarity)

`=> 27/(EF) = 15/(7.5)`

`=>` EF = 13.5 cm

Since EF || AB, ΔCEF ∼ ΔCAB

`=> (EC)/(AC) = (EF)/(AB)`

`=> 22.5/(AC) = 13.5/22.5`

`=>` AC = 37.5 cm