question_answer

What is the ratio of side and height of and equilateral triangle?

A) \[2:1\]                   

B)        \[1:1\]

C) \[2:\sqrt{3}\]  

D)        \[\sqrt{3\text{ }}:2\]

E) None of these

Correct Answer: C

Solution :

Explanation Option [c] is correct. \[A{{B}^{2}}=\text{ }B{{D}^{2}}+A{{D}^{2}}\] (Pythagoras theorem) \[{{a}^{2}}={{h}^{2}}+{{\left( \frac{9}{2} \right)}^{2}}\] \[\Rightarrow \,{{h}^{2}}=\frac{2}{3}{{a}^{2}}\Rightarrow \,h=\frac{\sqrt{3}}{2}a\] \[\frac{a}{h}=\frac{2}{\sqrt{3}}\]