Question

The area of an equilateral triangle is $9\sqrt{3} m^2$ . The length (in m) of the median is

• A. $$2\sqrt{3}m$$
• B. $$3\sqrt{3}m$$
• C. $$3\sqrt{2}m$$
• D. $$2\sqrt{2}m$$

Answer 1

Answer:

$$3\sqrt{3}m$$

$\frac{\sqrt{3}}{4}\times{(side)^2}=9\sqrt{3}$

=>Side^2=9\times{4}=36

=>side=\sqrt{36}=6metre

$BD=3metre$

$AD=\sqrt{AB^2-BD^2}=\sqrt{6^2-3^2}$

$=\sqrt{36-9}=\sqrt{27}$

$=3\sqrt{3}metre$