Question

Figure ABCD is a parallelogram

Answer 1

The answer would be C. 44 units. 

Answer 2

The first thing we must do for this case is to find the relationship between the variables.

We have then:

$AB = DC\\4y - 2 = 2y + 6$

From here, we clear the value of "Y":

$4y - 2y = 6 + 2\\2y = 8$

$y = \frac{8}{2}\\y = 4$

On the other hand we have:

$AD = BC\\3x - 1 = 2x + 2$

From here, we clear the value of "x":

$3x - 2x = 2 + 1\\x = 3$

Then, replacing values we have:

$AB = DC = 4y - 2 = 4 (4) - 2 = 16 - 2 = 14\\AB = DC = 14$

On the other hand:

$AD = BC = 2x + 2 = 2 (3) + 2 = 6 + 2 = 8\\AD = BC = 8$

Finally, the perimeter is given by:

$P = AB + DC + AD + BC$

Substituting values we have:

$P = 14 + 14 + 8 + 8\\P = 44$

Answer:

the perimeter of ABCD is:

44 units