Question

Given: ABCD is a parallelogram m∠A = 60º ; BK ⊥ AD AK = KD; Perimeter of ABCD = 24 Find: BD.

Answer 1

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 $y=0.5x$
Plug in the first equation we get: 
$2x+4(0.5x)=24\\2x+2x=24\\4x=24\\x=6$
We deduce that $BD=6.$