In an equilateral triangle ABC, if AD is
perpendicular to BC then
(A) ZAB2 = 3AD2 (B) 4AB2 = 3AD2
(C) 3AB2 = 2AD2 (D) 3AB2 = 4AD2
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Answer:
Given:
A ∆ ABC, in which sides are AB=BC= AC= a units
and AD is perpendicular to BC ,
In ∆ADB ,
AB²= AD²+ BD² (by Pythagoras theorem)
a² = AD² + (a/2)² [BD= 1/2BC, since in an equilateral triangle altitude AD is perpendicular bisector of BC ]
a²- a²/4 =AD²
=( 4a²-a²)/4 = AD²
= 3a² /4 = AD²
3AB²/4= AD²
[ AB= a]
3AB²= 4AD²
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