Question

figure abcd is a parallelogram.
what is the perimeter of abcd?
14 units
38 units
44 units
49 units

Explanation:

Step1: Use property of parallelogram (opposite sides equal)

In a parallelogram \(ABCD\), \(AD = BC\) and \(AB=CD\).
For \(AD = BC\): \(3x - 1=2x + 2\)
Subtract \(2x\) from both sides: \(3x-2x-1=2x - 2x+ 2\)
\(x-1 = 2\)
Add \(1\) to both sides: \(x=2 + 1=3\)
For \(AB = CD\): \(4y-2=2y + 6\)
Subtract \(2y\) from both sides: \(4y-2y-2=2y-2y + 6\)
\(2y-2=6\)
Add \(2\) to both sides: \(2y=6 + 2=8\)
Divide both sides by \(2\): \(y=\frac{8}{2}=4\)

Step2: Find the lengths of sides

Substitute \(x = 3\) into \(AD=3x - 1\): \(AD=3\times3-1=9 - 1=8\)
Substitute \(y = 4\) into \(AB=4y-2\): \(AB=4\times4-2=16 - 2=14\)

Step3: Calculate the perimeter

Perimeter of parallelogram \(P = 2(AB + AD)\)
\(P=2(14 + 8)\)
\(P=2\times22\)
\(P = 44\)

Answer:

44 units