Question

In triangle ABC, AB= BC = CA and AD = BC=CA. Then
AD^2 is equal to
(a) 1/2DC^2
(b) DC
(c) 2DC^2
(d) 3DC^2​

Answer 1

Answer:

Answer

Correct option is

C

3CD

2

Given, equilateral triangle ABC, AD⊥BC

Since, it is an equilaateral triangle, the perpendicualr also bisects the side.

Hence, BD=DC or BD=

2

1

BC=

2

1

AB

Now, In △ABD, we have

AB

2

=AD

2

+BD

2

⇒AB

2

−BD

2

=AD

2

⇒BC

2

−BD

2

=AD

2

⇒(2CD)

2

−CD

2

=AD

2

⇒3CD

2

=AD

2