SATHEE: Quantitative Aptitude Ques 2492

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.

Quantitative Aptitude Ques 2491

Quantitative Aptitude Ques 2493

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