MCQ
The area of an equilateral triangle is $81\sqrt{3}\text{cm}^2.$ Its height is:
- A$9\sqrt{3}\text{cm}$
- B$6\sqrt{3}\text{cm}$
- C$18\sqrt{3}\text{cm}$
- D$9\text{cm}$
Solution:
Area of quadrilateral triangle $=81\sqrt{3}\text{cm}^2$
$\Rightarrow\frac{\sqrt{3}}{4}\times(\text{Side})^2=81\sqrt{3}$
$\Rightarrow(\text{Side})^2=81\times4$
$\Rightarrow(\text{Side})^2=324$
$\Rightarrow\text{Side}=18\text{cm}$
Now,
$\text{Height}=\frac{\sqrt{3}}{2}\times\text{Side}=\frac{\sqrt{3}}{2}=9\sqrt{3}\text{cm}$
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