Question

In an equilateral triangle ABC, AD is an altitude. Then AD2 is equal to
A.3AB2
B.4AB2
C. 3/4 AB2
D.4/3 AB2

Answer 1

Step-by-step explanation:

Given, ABC is a equilateral triangle

So, AB=BC=CA=a (let)

In ΔABD and ΔACD

AB=AC and AD=AD

∠ADB=∠ADC

∴ΔABD≅ΔACD

Thus BD=CD=

2

a

Now in ΔABD∠D=90

0

⇒AB

2

=BD

2

+AD

2

=[

2

CD

]

2

=AD

2

⇒3AB

2

=4AD

2