question_answer

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

A) \[\sqrt{15}\,a\] unit

B) \[\frac{\sqrt{15}}{2}\,a\]unit

C) \[\sqrt{17}\,a\]unit

D) \[\frac{\sqrt{17}}{2}\,a\] unit

Correct Answer: B

Solution :

[b] \[A{{D}^{2}}=A{{B}^{2}}-B{{D}^{2}}=4{{a}^{2}}-\frac{{{a}^{2}}}{4}\] \[AD=\sqrt{\frac{15{{a}^{2}}}{4}}=\frac{a}{2}\sqrt{15}\,\text{units}\]