Erik draws quadrilateral ABCD

Question

. If side AB=40x , side BC=4+3y , side CD=8x+32 , and side AD=9y−20 , for what values of x and y can Erik be sure that his quadrilateral is a parallelogram?(1 point)
Responses

x=40 and y=16
x=1 and y=4
x=4 and y=1
x=20 and y=8

Answer 1

For a quadrilateral to be a parallelogram, its opposite sides must be equal in length.

In this case, AB = CD and BC = AD.
So we can set up the following equations:

40x = 8x + 32
40x - 8x = 32
32x = 32
x = 1

4 + 3y = 9y - 20
20 + 3y = 9y
20 = 6y
y = 20/6
y = 10/3

Therefore, the values of x and y that make the quadrilateral a parallelogram are x = 1 and y = 10/3.

However, none of the provided answer choices match this result.