Question

Figure ABCD is a parallelogram.

What is the perimeter of ABCD?

A. 14 units
B. 38 units
C. 44 units
D. 49 units

Answer 1

Answer: The answer is (C) 44 units.

Step-by-step explanation: ABCD is a parallelogram in the given figure, where the lengths of the sides are

AB = 4y - 2, BC = 2x + 2, CD = 2y + 6 and DA = 3x - 1.

We know that the opposite sides of a parallelogram are equal, so we ahve

AB = CD and BC = DA.

Therefore, we have

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

and

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

So, x = 3 and y = 4.

Hence, the perimeter will be

`p=AB+BC+CD+DA=4y-2+2x+2+2y+6+3x-1=5x+6y+5\\\\\Rightarrow p=5* 3+6* 4+5=15+24+5=44.`

Thus, the correct option is (C) 44 units.

Answer 2

3x-1 = 2x +2

3x = 2x +3

x = 3

3(3)-1 = 8

2(3) +2 = 8

4y-2 = 2y+6 =

4y=2y +8

2y = 8

y = 4

4(4)-2 = 14

2(4) +6 = 14

14 +14 + 8+ 8 =44 units

C is the correct answer