Quantitative Aptitude Ques 1323

Question: $ \Delta ABC $ is an isosceles triangle and $ \overline{AB}=\overline{AC}=2a $ units, $ \overline{BC}=a $ unit. Draw $ AD\bot BC $ and find the length of $ \overline{AD}. $

Options:

A) $ \sqrt{15}aunits $

B) $ \frac{\sqrt{15}}{2},aunits $

C) $ \sqrt{17}aunits $

D) $ \sqrt{\frac{17}{2},}aunits $

Show Answer

Answer:

Correct Answer: B

Solution:

  • $ AD^{2}=AB^{2}-BD^{2}=4a^{2}-\frac{a^{2}}{4} $ $ AD=\sqrt{\frac{15a^{2}}{4}}=\frac{a}{2}\sqrt{15}units $