Question

In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3
BC. Prove that 9 AD2= 7 AB2​

Answer 1

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=

2

1

BC=

2

AB

=

6

3AB

and

ED=

6

BC

=

6

AB

∴ AD

2

=

36

AB

2

+AB

2

−

36

9AB

2

∴ 9AD

2

=7AB

2

Answer 2

Answer:

Check your answer please