question_answer

In equilateral triangle of. side 2a, the length of its altitude will be:

A)  \[a\sqrt{3}\]

B)  \[a\]

C)  \[3a\]

D)  \[{{a}^{2}}\]  

Correct Answer: A

Solution :

 In equilateral triangle all sides are equal. In\[\Delta ADB\] AD is a altitude so, In\[\Delta ADB\].\[\angle ADB\]is a right angle \[{{(AB)}^{2}}={{(AD)}^{2}}+{{(BD)}^{2}}\] \[{{(AD)}^{2}}={{(AB)}^{2}}-{{(BD)}^{2}}\] \[{{(AD)}^{2}}={{(2a)}^{2}}-{{(a)}^{2}}\] \[{{(AD)}^{2}}=4{{a}^{2}}-{{a}^{2}}\] \[{{(AD)}^{2}}=3{{a}^{2}},\] \[AD=\sqrt{3{{a}^{2}}}=a\sqrt{3}\]