Notifications
Clear all
Triangles
1
Posts
2
Users
0
Likes
201
Views
0
04/06/2021 12:31 pm
Topic starter
ABC is an equilateral triangle of side 2a. Find each of its altitudes.
1 Answer
0
04/06/2021 12:33 pm
Given, ABC is an equilateral triangle of side 2a.
Draw, AD ⊥ BC
In ΔADB and ΔADC,
AB = AC
AD = AD
∠ADB = ∠ADC [Both are 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