question_answer

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

A) \[2:1\]

B) \[1:1\]

C) \[2:\sqrt{\text{3}}\]

D) \[\sqrt{3}:2\]

E) None of these

Correct Answer: C

Solution :

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