Question

Erik draws quadalilateral 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 quadirlateral is a parallelogram.

x=1, y=4
x=1, y=4

x=4, y=1
x=4, y=1

x=32, y=6
x=32, y=6

x=6, y=32

Answer 1

For a parallelogram opposite sides are equal: set AB = CD and BC = AD.

40x = 8x + 32 → 32x = 32 → x = 1.
4 + 3y = 9y − 20 → 24 = 6y → y = 4.

So x = 1 and y = 4 (which checks: AB = CD = 40, BC = AD = 16).