Question

In the figure given below AB = 3 cm, AC = 5 cm and AD = 4 cm and D is the midpoint of BC. Then the length of BD is :

• A. 1 cm
• B. 2 cm
• C. 3 cm
• D. 4 cm

Answer 1

The correct option is A

1 cm

Since D is the mid-point of BC,

From Apollonius theorem,

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