Question

figure abcd is a parallelogram. what is the perimeter of abcd? 14 units 38 units 44 units 49 units a 4y - 2 b 3x - 1 2x + 2 d 2y + 6 c

Explanation:

1. Recall the properties of a parallelogram:

• In a parallelogram \(ABCD\), opposite - sides are equal. So, \(AB = CD\) and \(AD = BC\).
• Set up the equations based on the equal - side property:
• For the sides \(AB\) and \(CD\): \(4y−2 = 2y + 6\).
• Subtract \(2y\) from both sides: \(4y-2y-2=2y - 2y+6\), which simplifies to \(2y−2 = 6\).
• Add 2 to both sides: \(2y-2 + 2=6 + 2\), so \(2y=8\).
• Divide both sides by 2: \(y = 4\).
• For the sides \(AD\) and \(BC\): \(3x−1 = 2x + 2\).
• Subtract \(2x\) from both sides: \(3x-2x-1=2x-2x + 2\), which gives \(x-1 = 2\).
• Add 1 to both sides: \(x=3\).

1. Find the lengths of the sides:

• Substitute \(y = 4\) into the expression for \(AB\): \(AB=4y−2=4\times4−2=16 - 2=14\).
• Substitute \(x = 3\) into the expression for \(AD\): \(AD=3x−1=3\times3−1=9 - 1=8\).

1. Calculate the perimeter of the parallelogram:

• The perimeter \(P\) of a parallelogram is \(P = 2(AB + AD)\).
• Since \(AB = 14\) and \(AD = 8\), then \(P=2(14 + 8)=2\times22 = 44\) units.

Answer:

44 units