Question

In an equilateral triangle ABC, D is a point
on side BC such that BD =1/3 BC. Prove
that 9 AD2 = 7 AB?​

Answer 1

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Answer 2

Answer:

△ABC is an Equilateral triangle such that,

AB=BC=AC

Construction:

Draw an Altitude AE such that,

E lies on BC and

AE perpendicular to BC

In △AEB

By Pythagoras Theorem,

AB 2 =AE 2 +EB 2 .(1)

In △AED

By Pythagoras Theorem,

AD 2 =AE 2 +ED 2 .(2)

From 1) and 2)

AD 2 =ED 2 +AB 2 −EB 2 .(3)

Since, EB= 21 BC= 2AB = 63AB and ED= 6BC = 6AB

∴ AD 2= 36AB 2 +AB 2 − 369AB 2

∴ 9AD 2 =7AB 2