What values must x and y have to make the quadrilateral a parallelogram.

Question

Answer 1

The diagonals of any parallelogram must equal each other.

1. We have y^2 = y + 30 . In this case y = 6 or -5. This would make this diagonal 72 units long and 50 units long respectively.
2. We also have 3x-40 = x. In this case x =20 would make this diagonal 40 units long.

Answer 2

The diagonals would bisect each other if it were a parallelogram. That means "y²" would equal "y + 30" and "x" would equal "3x - 40".

If: y² = y + 30 then:

y² - y - 30 = 0

(y - 6)(y + 5) = 0

So either y - 6 = 0 (meaning y = 6) or y + 5 = 0 (meaning y = -5). If y = 6, then the diagonal would be 72 units long (each segment would be 36). If y = -5, then the diagonal would be 50 units long (each segment would be 25).

If: x = 3x - 40, then:

2x = 40 or x = 20.

If x = 20, then the diagonal would be 40 units long (each segment would be 20)