Question

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

Explanation:

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

In a parallelogram \(ABCD\), \(AD = BC\) and \(AB=CD\).
For \(AD = BC\):
\(3x - 1=2x + 2\)
\(3x-2x=2 + 1\)
\(x = 3\)
For \(AB = CD\):
\(4y-2=2y + 6\)
\(4y-2y=6 + 2\)
\(2y=8\)
\(y = 4\)

Step2: Calculate the lengths of the 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 of the parallelogram

The perimeter \(P\) of a parallelogram is \(P = 2(AB + AD)\)
\(P=2(14 + 8)\)
\(P=2\times22\)
\(P = 44\)

Answer:

44 units