Question

In the given figure, AB || EF || DC; AB = 67.5 cm, DC = 40.5 cm and AE = 52.5 cm.

1. Name the three pairs of similar triangles.
2. Find the lengths of EC and EF.

Answer 1

i. The three pair of similar triangles are:

∆BEF and ∆BDC

∆CEF and ∆CAB

∆ABE and ∆CDE

ii. Since, ∆ABE and ∆CDE are similar,

`(AB)/(CD) = (AE)/(CE)`

`(67.5)/(40.5) = (52.5)/(CE)`

CE = 31.5 cm

Since, ∆CEF and ∆CAB are similar,

`(CE)/(CA) = (EF)/(AB)`

`(31.5)/(52.5 + 31.5) = (EF)/67.5`

`(31.5)/84 = (EF)/67.5`

`EF = 2126.25/84`

`EF = 405/16 = 25 5/16 cm`