Question

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

Answer 1

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`