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In the Given Figure, De || Bd. Determine Ac and Ae. - Mathematics

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प्रश्न

In the given figure, DE || BD. Determine AC and AE.

योग

उत्तर

Given, `DE||CB`.

In ∆ABC and ∆ADE

`∠ ADE= ∠ C `  (Corresponding angles)

\[\angle A = \angle A\]  (Common)
`Δ ABC ∼ Δ ADE ` (AA Similarity)
`(AE)/4=12/15=14/(AC)`
`(AE)/4 =12/15`
`AExx15=12xx4`
`AE=(12xx4)/15`
`AE=(cancel(12^4)xx4)/cancel(15_5)`
`AE=(4xx4)/5`
`AE= 16/5`
`(AE)/4=12/15=14/(AC)`
`12/15=14/(AC)`
`12 xxAC=14xx15`
`AC= (14xx15)/12`
`AC=(7xxcancel2xx5xxcancel3)/(2xxcancel2xxcancel3)`
`AC =35/2`

Hence the value of  AC and AE is  `35/2` and `16/5`

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अध्याय 7: Triangles - Exercise 7.8 [पृष्ठ १२३]

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आरडी शर्मा Mathematics [English] Class 10
अध्याय 7 Triangles
Exercise 7.8 | Q 4 | पृष्ठ १२३

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