3 Tutor System
Starting just at 265/hour

# ABC is an equilateral triangle of side 2a. Find each of its altitudes.

Given, ABC is an equilateral triangle of side 2a.

Draw, AD $$\perp$$ BC

In $$\triangle$$ ADB and $$\triangle$$ ADC,
AB = AC
$$\angle$$ ADB = $$\angle$$ ADC [Both are 90°]

Therefore, $$\triangle$$ ADB $${\displaystyle \cong }$$ $$\triangle$$ ADC by RHS congruence.
Hence, BD = DC [by CPCT]

In right angled $$\triangle$$ ADB,
$$AB^2 = AD^2 + BD^2$$
$$(2a)^2 = AD^2 + a^2$$
$$AD^2 = 4a^2 – a^2$$
$$AD^2 = 3a^2$$
$$AD = \sqrt{3} a$$