MCQ
The height of an equilateral triangle having each side $12cm$, is:
- A$6\sqrt{2}\text{ cm}$
- ✓$6\sqrt{3}\text{ cm}$
- C$3\sqrt{6}\text{ cm}$
- D$6\sqrt{6}\text{ cm}$
✓
Answer
Correct option: B.
$6\sqrt{3}\text{ cm}$
Let $\triangle\text{ABC}$ be the equilateral triangle and $AD$ be the height.
The height of an equilateral triangle is the same as its median.
So, $AD = 6m$
$\triangle\text{ABC}$ is a right-angled triangle.
By Pythagoras theorem,
$ \mathrm{AC}^2=\mathrm{AC}^2+\mathrm{AD}^2 $
$ \Rightarrow \mathrm{DC}^2=\mathrm{AC}^2-\mathrm{AD}^2 $
$ \Rightarrow \mathrm{DC}^2=12^2-6^2 $
$ \Rightarrow \mathrm{DC}^2=144-36 $
$ \Rightarrow \mathrm{DC}^2=108$
$\Rightarrow\text{DC}=\sqrt{3\times4\times9}$
$\Rightarrow\text{DC}=6\sqrt{3}\text{ cm}$
So, the height is $6\sqrt3\text{cm}.$
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