Question

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

Explanation:

Step1: Use the property of parallelogram perimeter

In a parallelogram, opposite sides are equal. So the perimeter \(P = 2\times(\text{side}_1+\text{side}_2)\). Here, \(P = 2\times[(2x + 9)+(x - 5)]\), and \(P = 50\) mm. Then \(2\times[(2x + 9)+(x - 5)]=50\).

Step2: Simplify the equation

First, simplify the expression inside the brackets: \((2x + 9)+(x - 5)=2x+x+9 - 5=3x + 4\). The equation becomes \(2\times(3x + 4)=50\), then \(3x+4=\frac{50}{2}=25\).

Step3: Solve for \(x\)

Subtract 4 from both sides: \(3x=25 - 4=21\). Divide both sides by 3: \(x=\frac{21}{3}=7\).

Step4: Find the length of \(WZ\)

Since \(WZ=2x + 9\), substitute \(x = 7\) into it. \(WZ=2\times7+9=14 + 9=23\) mm.

Answer:

C. \(23\) mm