Quantitative Aptitude Ques 2492
Question: If the median drawn on the base of a triangle is half its base, then the triangle will be
Options:
A) obtuse angled
B) equilateral
C) right angled
D) acute angled
Show Answer
Answer:
Correct Answer: C
Solution:
- Let ABC be a triangle and AD be the median Then, $ AD=\frac{1}{2}BC $ Now, by Apollonius theorem $ AB^{2}+AC^{2}=2,(AD^{2}+BD^{2}) $ Since, $ AD=BD=DC $ $ =\frac{1}{2}BC $
$ \therefore $ $ AB^{2}+AC^{2}=2[ {{( \frac{BC}{2} )}^{2}}+{{( \frac{BC}{2} )}^{2}} ] $
$ \Rightarrow $ $ AB^{2}+AC^{2}=2( \frac{BC^{2}}{4}+\frac{BC^{2}}{4} ) $
$ \Rightarrow $ $ AB^{2}+AC^{2}=2( \frac{BC^{2}}{2} ) $
$ \Rightarrow $ $ AB^{2}+AC^{2}=BC^{2} $ Here, it follows Pythagoras theorem. So, it is a right angled triangle.
BETA
