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Figure ABCD is a parallelogram.

Parallelogram A B C D is shown. The length of A B is 4 y minus 2, the length of B C is 2 x + 2, the length of D C is 2 y + 6, and the length of A D is 3 x minus 1.

What is the perimeter of ABCD?

14 units
38 units
44 units
49 units

Respuesta :

Answer:

It is 44

Step-by-step explanation:

akposevictor

The perimeter of the paralllelogram given is: 44 units.

What is the Perimeter of a Parallelogram?

Perimeter = 2(a + b), where a and b are the legs of the sides adjacent to each other.

Given the following:

  • AB = 4y - 2
  • BC = 2x + 2
  • DC = 2y + 6
  • AD = 3x - 1

Since opposite sides of a parallelogram are equal, therefore:

4y - 2 = 2y + 6

4y - 2y = 2 + 6

2y = 8

y = 4

2x + 2 = 3x - 1

2x - 3x = -2 - 1

-x = -3

x = 3

Perimeter of the paralllelogram = 2(AB + AD) = 2(4y - 2 + 3x - 1)

Plug in the values of x and y

Perimeter of the paralllelogram = 2(4(4) - 2 + 3(3) - 1)

Perimeter of the paralllelogram = 2(16 - 2 + 9 - 1)

Perimeter of the paralllelogram = 44 units.

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