Question

If in ∆ABC,DE||BC ,AD by DB = 3 by 5 and AC=4.8,then the length of AE is? a)8cm b) 3.2cm c) 1.6cm d)1.8 cm.​

Answer 1

In ∆ABC, DE || BC

$\frac{AD}{DB} = \frac{AE}{EC} ...1 \\ \\\frac{AD+DB}{DB} = \frac{AE + EC}{EC} .... \: by \: componendo \\ \\ \frac{AB}{DB} = \frac{AC}{EC} \\ \\ \frac{8}{5} = \frac{4.8}{EC} \\ \\ 8 \times EC = 5 \times 4.8 \\ EC = 3 \\ \\ \: by \: equation \: 1 \\ \\ \frac{AD}{DB} = \frac{AE}{EC} \\ \\ \frac{3}{5} = \frac{AE}{3} \\ \\ 3 \times 3 = 5 \times AE \\ 9 = 5 \times ae \\ \\ \frac{9}{5} = AE \\ 1.8 = AE$

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