y shouldn't we plot AD on RHS
proper answer is needed
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Solution :
This Question has taken from the triangle chapter of class 10th CBSE . Well , your question is a general question . Let us clarify the doubt along with prove of 9AD^2 = 7AB^2 where BD = 1/3 BC .
Question :
In a equilateral triangle ABC , D is a point on side BC such that BD = 1/3 BC . Prove that 9AD^2 = 7AB^2 ?
Answer :
At the very initial stage we draw a figure of it . Make a equilateral triangle ABC . Now , according to the question" D is a point on BC " It means that a perpendicular can be drawn from A to D and from AD we construct the point E . We can also suppose AE is a perpendicular where A can be extended to D . This is a basic that we can't consider AD on R.H.S according to our earlier classes concepts . We say ABCDE not ABCED . According to the data provided to us that BD = 1/3 BC . After take a Glance at the figure let us begin the proof .
Given :
BD = 1/3 BC
Δ ABC is an equilateral triangle
To Prove :
9AD^2 = 7AB^2
Construction :
Draw AE ⊥ BC
Proof :
In Δ ADE
⇒ AD^2 = AE^2 + DE^2 --> 1
In Δ ABE
⇒ AB^2 = AE^2 + BE^2 --> 2
From equation (1) and (2)
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