Question

the perimeter of parallelogram wxyz is 50 millimeters. what is wz? 2 mm 7 mm 23 mm 25 mm

Explanation:

1. Recall the property of a parallelogram:

• In a parallelogram, opposite - sides are equal. So, in parallelogram \(WXYZ\), \(WX = ZY=(2x + 9)\text{ mm}\) and \(XY = WZ=(x - 5)\text{ mm}\).
• The perimeter \(P\) of a parallelogram is given by \(P = 2(WX+WZ)\).
• We know that \(P = 50\text{ mm}\), so \(2((2x + 9)+(x - 5))=50\).

1. Simplify the equation:

• First, simplify the expression inside the parentheses: \((2x + 9)+(x - 5)=2x+9+x - 5=3x + 4\).
• Then the equation becomes \(2(3x + 4)=50\).
• Divide both sides of the equation by 2: \(3x + 4 = 25\).
• Subtract 4 from both sides: \(3x=25 - 4=21\).
• Divide both sides by 3: \(x = 7\).

1. Find the length of \(WZ\):

• Since \(WZ=x - 5\) and \(x = 7\), then \(WZ=7 - 5=2\text{ mm}\).

Answer:

A. 2 mm