Question

figure abcd is a parallelogram. what are the lengths of line segments ab and bc? ab = 4; bc = 16 ab = 4; bc = 8 ab = 10; bc = 20 ab = 10; bc = 28

Explanation:

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

In a parallelogram \(ABCD\), \(AD = BC\) and \(AB=CD\).
For \(AD = BC\): \(2x - 4=x + 12\).
Solve the equation \(2x - 4=x + 12\):
Subtract \(x\) from both sides: \(2x-x-4=x - x+ 12\), so \(x-4 = 12\).
Add \(4\) to both sides: \(x=12 + 4=16\).
For \(AB = CD\): \(3y-2=y + 6\).
Solve the equation \(3y-2=y + 6\):
Subtract \(y\) from both sides: \(3y-y-2=y - y+ 6\), so \(2y-2 = 6\).
Add \(2\) to both sides: \(2y=6 + 2=8\).
Divide both sides by \(2\): \(y = 4\).

Step2: Calculate the lengths of \(AB\) and \(BC\)

Substitute \(y = 4\) into \(AB=3y - 2\): \(AB=3\times4-2=12 - 2=10\).
Substitute \(x = 16\) into \(BC=x + 12\): \(BC=16+12=28\).

Answer:

\(AB = 10\); \(BC = 28\) (the fourth option)