figure abcd is a parallelogram. what is the perimeter of abcd? a 4y - 2 b 3x - 1 2x + 2 d 2y + 6 c 14 units…

Answer:

C. 44 units

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite - sides are equal. So, $AB = CD$ and $AD = BC$. $4y−2=2y + 6$ and $3x−1=2x + 2$.

Step2: Solve for $y$

$4y−2y=6 + 2$, $2y=8$, $y = 4$.

Step3: Solve for $x$

$3x-2x=2 + 1$, $x = 3$.

Step4: Find side - lengths

$AB=4y−2=4\times4−2=14$. $BC=2x + 2=2\times3+2=8$.

Step5: Calculate perimeter

Perimeter of parallelogram $ABCD=2(AB + BC)=2(14 + 8)=2\times22 = 44$ units.