ABCD is a parallelogram. its perimeter is 20 cm. if (^ABD)=60, BD=8 CM, calculate AB, AD.

ABCD is a parallelogram.

Also
given the perimeter  AB+BC+CD+AD = 20 cm

Therefore AB+AD =
1/2 (20 cm) = 10 cm, as opposite sides of a parallelogram are equal in
length.

Let AB = X. Then AD = 10-x. Given BD = 8 cm, angle
ABD = 60 deg.

We apply cosine rule for triangle
ABD:

AB^2+BD^2- 2AB*BD =
AD^2.

x^2+8^2-2*x*8*cos60 =
(10-x)^2

x^2+64-2*x*8*(1/2) =
(10-x)^2

x^2+64-8x =
10^2-20x+x^2.

=> 64-8x =
100-20x.

=> 20x - 8x = 100-64 =
36

=> 12x =
36

=> x = 36/12 = 3. Or AB = 3 cm. So AM = (10-x)cm
= (10 -3) cm = 7 cm.

Therefore AB = 3cm. AD =
7 cm.