To find the value of x in the rhombus ABCD, we can use the formula for the area of a rhombus, which is given by:
Area = (d1 * d2) / 2
where d1 and d2 are the lengths of the diagonals. In this case, we have:
d1 = EC = 8 units
d2 = DB = x units
According to the problem, the area is 72 square units. Substituting the known values into the area formula gives us:
72 = (8 * x) / 2
To get rid of the fraction, we can multiply both sides by 2:
144 = 8 * x
Now, we can solve for x by dividing both sides by 8:
x = 144 / 8
x = 18
Therefore, the value of x is 18 units.