Question

in an equilateral triangle abc if ad perpendicular bc then​

Answer 1

Step-by-step explanation:

△ABC is a equilateral triangle.

Thus, AB=BC=AC and∠ABC=∠BAC=∠ACB=60

∠ADB=∠ADC=90

In △ABD,∠BAD+∠ABD+∠ADB=180

⇒∠BAD=180−90−60=30

Similarly for △ACD,∠CAD+∠ACD+∠ADC=180

⇒∠CAD=180−90−60=30

Now, In △ABD and △ACD

AB=AC

∠BAD=∠CAD

AD=AD(Common side)

Thus, △ABD and △ACD are congruent.(SAS)

Therefore BD=DC=

2

1

BC=

2

1

AB

Now, △ABD is a right angled triangle.

Therefore

AB

2

=BD

2

+AD

2

⇒AB

2

=(

2

1

AB)

2

+AD

2

⇒AB

2

=

4

AB

2

+AD

2

⇒AB

2

−

4

AB

2

=AD

2

⇒

4

4AB

2

−AB

2

=AD

2

⇒3AB

2

=4AD

2