Question

ABC is an equilateral triangle of side 6 cm. The length of its altitude is

• A. $3$ cm
• B. $\sqrt{3}$ cm
• C. $6\sqrt{3}$ cm
• D. $3\sqrt{3}$ cm

Answer 1

The correct option is C $6\sqrt{3}$ cm

ABC is an equilateral triangle of side 6 cm. Let AM be its altitude.


Area of an equilateral triangle of side 6 cm is
$\frac{\sqrt{3}}{2}\times (side{)}^2=\frac{\sqrt{3}}{2}\times (6{)}^2=18\sqrt{3}c{m}^2$......(i)
Also, area of $\Delta ABC=\frac{1}{2}\times Base\times Height$
$\Rightarrow$ Area of $\Delta ABC=\frac{1}{2}\times BC\times AM$
$=\frac{1}{2}\times 6\times AM$ ..........(ii)
Thus, from (i) and (ii),
$=\frac{1}{2}\times 6\times AM=18\sqrt{3}$
$\Rightarrow AM=6\sqrt{3}$
Hence, the correct answer is option (c).