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ABC is an equilateral triangle of side 2a. Find each of its altitudes. |
Answer» ABC is an equilateral triangle of side 2a. Draw, AD ⊥ BC In ΔADB and ΔADC, we have AB = AC [Given] AD = AD [Given] ∠ADB = ∠ADC [equal to 90°] Therefore, ΔADB ≅ ΔADC by RHS congruence. Hence, BD = DC [by CPCT] In right angled ΔADB, AB2 = AD2 + BD2 (2a)2 = AD2 + a2 ⇒ AD2 = 4a2 - a2 ⇒ AD2 = 3a2 ⇒ AD = √3a |
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