Question

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?

Answer 1

44

Explanation:

Answer 2

Perimeter of ABCD = 44.

Explanation:

If Figure ABCD is a parallelogram, then its opposite sides are equal in length.

Perimeter of parallelogram ABCD = 2 ( sum of its adjacent sides)

Now since ABCD is a parallelogram then, AB = CD and BC = AD.

Given:
`AB = 4y-2, BC = 2x + 2, CD = 2y + 6 and AD = 3x-1`

Now since
`AB = CD\ \ therefore,`

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

In the same way,
`BC = AD, therefore`

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

Now perimeter of ABCD =
`2(AB + BC)`

=
`2( 4y-2 +2x+2)`

=
`2(4y+2x)`

Now by substituting the values of x and y in above expression,

`2(4y+2x) \\2\left (4(4)+2(3) \right )\\2(16+6) =2(22) = 44`