Question

the perimeter of parallelogram wxyz is 50 millimeters. what is wz? (2x + 9) mm (x - 5) mm w z y not drawn to scale 2 mm 7 mm 23 mm

Explanation:

Step1: Recall property of parallelogram

In parallelogram WXYZ, WX = ZY and WZ = XY. Let WX=(2x + 9)mm and XY=(x - 5)mm. The perimeter formula for a parallelogram is $P = 2(WX+XY)$.

Step2: Substitute into perimeter formula

We know that $P = 50$mm. So, $50=2((2x + 9)+(x - 5))$.
First, simplify the expression inside the parentheses: $(2x + 9)+(x - 5)=2x+x+9 - 5=3x + 4$. Then the equation becomes $50 = 2(3x + 4)$.

Step3: Solve the equation for x

Distribute the 2 on the right - hand side: $50=6x + 8$.
Subtract 8 from both sides: $50−8=6x$, so $42 = 6x$.
Divide both sides by 6: $x=\frac{42}{6}=7$.

Step4: Find the length of WZ

Since WZ = XY and XY=(x - 5)mm, substitute x = 7 into the expression for XY. Then XY=(7 - 5)mm = 2mm. So WZ = 2mm.

Answer:

2 mm