Question

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 38 units 44 units 49 units

Explanation:

Step1: Use property of parallelogram

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

Step2: Solve for $y$

For the equation $4y−2 = 2y + 6$, subtract $2y$ from both sides:
$4y-2y-2=2y-2y + 6$, which simplifies to $2y-2 = 6$.
Then add 2 to both sides: $2y-2 + 2=6 + 2$, so $2y=8$, and $y = 4$.

Step3: Solve for $x$

For the equation $3x−1=2x + 2$, subtract $2x$ from both sides:
$3x-2x-1=2x-2x + 2$, so $x-1 = 2$.
Add 1 to both sides: $x-1 + 1=2 + 1$, and $x = 3$.

Step4: Find the side - lengths

Substitute $y = 4$ into the expression for $AB$: $AB=4y−2=4\times4−2=16 - 2=14$.
Substitute $x = 3$ into the expression for $AD$: $AD=3x−1=3\times3−1=9 - 1=8$.

Step5: Calculate the perimeter

The perimeter $P$ of a parallelogram is $P = 2(AB + AD)$.
$P=2(14 + 8)=2\times22 = 44$ units.

Answer:

44 units