Answer: The unknown side measures 7.2 units
Step-by-step explanation: This question clearly shows two parallelograms. As shown in the attached diagram, the bigger one is ABCD while the smaller one is EFGH.
Since they are similar figures, and they are placed at the same angle, we can see that one parallelogram is congruent with the other, that is, ABCD is congruent with EFGH. With that fact in mind, we can now find the similar ratios between both figures.
We can say therefore that,
AD/BC = EH/FG
Note that AB = DC and therefore AD = BC. That means BC = 10 units
Similarly EH = FG and therefore EF = HG. That means EH = 6 units
So with this bit of information we can also say that,
AB/AD = EF/EH
12/10 = EF/6
By cross multiplication we now have 12 x 6 = EF x 10
72 = EF x 10
Divide both sides of the equation by 10
7.2 = EF
And since we have determined that EF = HG,
Line HG = 7.2 units