For what values of x and y must this quadrilateral be a parallelogram? Find length of the sides. 4x = top, 6y = right, 3y+19 is bottom, and 2x +4 is the left.

Question

How to determine x and y values in the sides of a quadrilateral for it to be a parallelogram.

Answer 1

In a parallelogram, the opposite sides' lengths need to equal one another. So:

4x = 3y + 19 (top and bottom)

2x + 4 = 6y (left and right)

 

Let's move the variables to one side and constants to the other:

4x - 3y = 19

-2x + 6y = 4

 

We now have a pair of equations that can be manipulated to use the elimination method. Multiply the first equation by 2:

8x - 6y = 38

-2x + 6y = 4

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6x = 42

Divide by 6:

x = 7

 

Find y:

4 * 7 = 3y + 19

28 = 3y + 19

9 = 3y

3 = y

 

check:

2 * 7 + 4 = 6 * 3

14 + 4 = 18

18 = 18

 

so x is 7 and y is 3.