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Question
In the given figure, AB || EF || DC; AB = 67.5 cm, DC = 40.5 cm and AE = 52.5 cm.
- Name the three pairs of similar triangles.
- Find the lengths of EC and EF.
Solution
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`
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