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In an equilateral triangle ABC, if AD ⊥ BC, then:
- a)2AB2 = 3AD2
- b)4AB2 = 3AD2
- c)3AB2 = 4AD2
- d)None of the above
Correct answer is 'C'. Can you explain this answer?
Verified Answer
In an equilateral triangle ABC, if AD ⊥BC, then:a)2AB2= 3AD2b)4AB...
Δ ABC is an equilateral triangle
By Pythagoras theorem in triangle ABD
AB2 = AD2 + BD2
but BD = 1/2 BC (∵ In a triangle, the perpendicular from the vertex to the base bisects the base)
thus AB2 = AD2 + {1/2 BC}2
AB2 = AD2 + 1/4 BC2
4 AB2 = 4AD2 + BC2
4 AB2 - BC2 = 4 AD2
(as AB = BC we can subtract them )
Thus 3AB2 = 4AD2
Most Upvoted Answer
In an equilateral triangle ABC, if AD ⊥BC, then:a)2AB2= 3AD2b)4AB...
Given:
A ∆ ABC, in which sides are AB=BC= AC= a units
and AD is perpendicular to BC ,
In ∆ADB ,
AB^2= AD^2+ BD^2 (by Pythagoras theorem)
a^2 = AD^2 + (a/2)^2 [BD= 1/2BC, since in an equilateral triangle altitude AD is perpendicular bisector of BC ]
a^2- a^2/4 =AD^2
=( 4a^2-a^2)/4 = AD^2
= 3a^2 /4 = AD^2
3AB^2/4= AD^2
[AB = a]
3AB^2= 4AD^2
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In an equilateral triangle ABC, if AD ⊥BC, then:a)2AB2= 3AD2b)4AB...
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