Question

Erik draws quadrilateral ABCD 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)
x=1 and y=4
x=20 and y=8
x=40 and y=16
x=4 and y=1

Answer 1

To determine if a quadrilateral is a parallelogram, we need to compare the opposite sides of the quadrilateral.

In this case, we need to compare sides AB and CD, as well as sides BC and AD.

For a quadrilateral to be a parallelogram, the opposite sides must be equal.

Comparing sides AB and CD:

AB = 40x
CD = 8x + 32

For AB and CD to be equal, we need to set up the following equation:

40x = 8x + 32

Simplifying the equation:

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

Comparing sides BC and AD:

BC = 4 + 3y
AD = 9y - 20

For BC and AD to be equal, we need to set up the following equation:

4 + 3y = 9y - 20

Simplifying the equation:

3y - 9y = -20 - 4
-6y = -24
y = 4

Therefore, the values of x and y that make Erik's quadrilateral a parallelogram are:

x = 1 and y = 4

So the correct answer is:

x = 1 and y = 4