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

Explanation:

Step1: Use the property of parallelogram (opposite sides are equal)

In a parallelogram \(ABCD\), \(AB = CD\) and \(BC=AD\).
So, we have the equations:
\(40x=8x + 32\) (because \(AB = CD\))
\(4 + 3y=9y-20\) (because \(BC = AD\))

Step2: Solve the equation \(40x=8x + 32\)

Subtract \(8x\) from both sides:
\(40x-8x=8x + 32-8x\)
\(32x=32\)
Divide both sides by \(32\):
\(x = 1\)

Step3: Solve the equation \(4 + 3y=9y-20\)

Subtract \(3y\) from both sides:
\(4+3y - 3y=9y-20 - 3y\)
\(4 = 6y-20\)
Add \(20\) to both sides:
\(4 + 20=6y-20+20\)
\(24 = 6y\)
Divide both sides by \(6\):
\(y = 4\)

Answer:

\(x = 1\) and \(y = 4\)