Question

ABC is an equilateral triangle of side 2a. Then the length each of its altitude is

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

Answer 1

The correct option is C

$\sqrt{3}a$

It is given that ABC is an equilateral triangle of side 2a

Draw $\text{AD}\perp \text{BC}$. [Altitudes are perpendiculars drawn from a vertex to its opposite side and they bisect the opposite side in a equilateral triangle]

$\Rightarrow \Delta \text{ADB},\Delta \text{ADC}$ are right-angled triangles.

In right angled $\Delta \text{ADB}$,

$A{B}^2=A{D}^2+B{D}^2$

$(2a{)}^2=A{D}^2+a^2$

$\Rightarrow A{D}^2=4a^2-a^2$

$\Rightarrow A{D}^2=3a^2$

$\Rightarrow AD=\sqrt{3}a$

$\therefore$ Length of each altitue is $\sqrt{3}a$