Question

In the figure given below AB = 3, AC = 5 and AD = 4. Then, BD = (AD is median and AE is perpendicular to BC)

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is A

1

Since D is the midpoint of BC, using Appollonian thorem

$A{B}^2+A{C}^2=2(B{D}^2+A{D}^2)3^2+5^2=2(B{D}^2+4^2)\left(\frac{9+25}{2}\right)=B{D}^2+16\Rightarrow B{D}^2=17-16\Rightarrow BD=1cm$