Question

In triangle ABC,D is a point on BC such that 3BD=BC. If each side of the triangle is 12cm,then AD equals ​

Answer 1

Answer:

Step-by-step explanation:

                                  /\A

                               /  l   \

                            /     l      \

                         /        l         \      join AD

                      /.............l.....,......\

                    C           P    D    B

draw a perpendicular AP.

AB=BC=CA=12 cm      given

let BD= x cm

3x=12

x=4=BD

BP=PC..............................equilateral triangle therefore perpendicular from any

                                     vertex bisects the opposite side

PC=6cm=PB

therefore PD=PB-BD=6-4=2

now to find AD

lets calculate the length of the perpendicular AP using pythagoras theorem

AP²+AB²=PB²

AP²+12²= 6²

AP²=144-36

AP=√108

AP=6√3

in triangle APD

AP²+PD²=AD²

(6√3)² + 2² = AD²

AD²= 108+4

AD = √112

AD=4√7 cm