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
    $9\text{cm}$

Answer

  1. $9\sqrt{3}\text{cm}$

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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