Question

figure abcd is a parallelogram. what is the perimeter of abcd? 14 units 38 units 44 units 49 units a 4y - 2 b 3x - 1 2x + 2 d 2y + 6 c

Explanation:

Step1: Opposite sides of parallelogram are equal.

AB = CD: $4y - 2 = 2y + 6$; AD = BC: $3x - 1 = 2x + 2$

Step2: Solve for y.

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

Step3: Solve for x.

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

Step4: Calculate AB length.

AB = $4y - 2 = 4(4) - 2 = 14$

Step5: Calculate AD length.

AD = $3x - 1 = 3(3) - 1 = 8$

Step6: Perimeter = 2*(AB + AD).

Perimeter = $2*(14 + 8) = 44$

Answer:

C. 44 units