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. $
BETA
