SATHEE: Quantitative Aptitude Ques 1636

Quantitative Aptitude Ques 1636

Question: In $ \Delta ABC, $ $ DE||BC, $ $ AD=2.5,cm, $ $ DB=5,cm, $ $ AE=2,cm $ and $ BC=2cm. $ Find EC and DE respectively. 5 cm

Options:

A) 4 cm and 3 cm

B) 5 cm and 3 cm

C) 2 cm and 4 cm

D) 4 cm and 5 cm

Show Answer

Answer:

Correct Answer: A

Solution:

[a] In $ \Delta ADE $ and $ \Delta ABC, $ $ \angle ADE=\angle ABC $ [ $ \because DE\parallel BC $ and AB is a transversal i.e. corresponding angle] $ \angle AED=\angle ACB $ [ $ \because DE\parallel BC $ and AB is a transversal i.e. corresponding angle] $ \angle A=\angle A $ [common]

$ \therefore $ $ \Delta ADE\sim \Delta ABC $ So, $ \frac{AD}{AB}=\frac{AE}{AC} $
$ \Rightarrow $ $ \frac{2.5}{7.5}=\frac{2}{AC} $

$ \Rightarrow $ $ AC=\frac{2\times 75}{25}=6 $

$ \therefore $ $ EC=AC-AE=6-2=4,cm $ and $ \frac{AD}{AB}=\frac{DE}{BC} $
$ \Rightarrow $ $ \frac{2.5}{7.5}=\frac{DE}{9} $

$ \Rightarrow $ $ DE=9\times \frac{25}{75}=3,cm. $

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