Find x if ABCD is a parallelogram as given in figure below, with two diagonals AC and BD intersecting at O and OA =  x + 3, OB = y + 2, OC = 2x + y, OD = 3y

ABCD is a parallelogram.

Diagonals AC and BD intersect at O.

OA = x + 3, OB = y + 2, OC = 2x + y, OD = 3y.

In a parallelogram, the diagonals bisect each other.

Therefore:

OA = OC and OB = OD

OA = OC

x + 3 = 2x + y

2x – x + y = 3

x + y = 3…………….(i)

Now,

OB = OD

y + 2 = 3y

3y – y = 2

2y = 2

y = $$\frac{2}{2}$$​​

y = 1

Putting value of y in eqn(i)

x + y = 3

x + 1 = 3

x = 3 – 1

x = 2

Thus, value of x = 2