If ABC is an equilateral triangle with AD perpendicular to BC, then prove that AD2= 3CD2 - Maths - Triangles

Question

If ABC is an equilateral triangle with AD perpendicular to BC,
then prove that AD2= 3CD2

Ankush Jain · Accepted Answer

In right âˆ†ACD,

â‡’ AC2 = AD2 +
CD2

â‡’ BC2 = AD2 +
CD2 ( AB = BC = CA)

â‡’ (2CD)2 = AD2 +
CD2 ( BC = 2CD)

â‡’ 4CD2 = AD2 +
CD2

â‡’ AD2 = 4CD2
â€“ CD2

â‡’ AD2 = 3CD2

If ABC is an equilateral triangle with AD perpendicular to BC, then prove that AD2= 3CD2.