Respuesta :

Since AK =  KD, then the triangle ABD is isosceles,
Then BD = AB. Denote AB by x and AK by y. 
Then, 
2x+4y=24 (the perimeter)
cos 60=y/x. 
From the second equation we get [tex]y=0.5x[/tex]
Plug in the first equation we get: 
[tex]2x+4(0.5x)=24\\2x+2x=24\\4x=24\\x=6[/tex]
We deduce that [tex]BD=6.[/tex]

Answer:

Since AK =  KD, then the triangle ABD is isosceles,

Then BD = AB. Denote AB by x and AK by y.  

Then,  

2x+4y=24 (the perimeter)

cos 60=y/x.  

From the second equation we get  

Plug in the first equation we get:  

We deduce that

Step-by-step explanation: