Let ABCD be a parallelogram whose diagonals equations are: AC:x+2y=3; BD: 2x+y=3. if length of diagonal AC=4 units and area of ABCD =8 units. Find the length of BD, AB and BC.

Dear harshit

point of intersection of these two line are (1,1)

digonal cut each other at mid point

length of second digonal

area=1/2 *d1 *d2 *sinθ     where θ is angel between these two lines

   8 =1/2 *4 *d2 *3/5

d2=20/3

BD=20/3

now you can find the point on line AC which is at d1/2=2 unit in both the direction of point (1,1)

 these points will be A and C

similarly  you can find the point on line BD which is at d2/2=10/3 unit in both the direction of point (1,1)

 these points will be Band D

once you know the point you can easly find the length of sides