Question

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

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - sides are equal. So, $WX = YZ=(2x + 9)$ mm and $XY = WZ=(x - 5)$ mm.
The perimeter formula of a parallelogram is $P = 2(WX+WZ)$.

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: $(2x + 9)+(x - 5)=2x+x+9 - 5=3x + 4$.
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 $WZ=x - 5$ and $x = 7$, then $WZ=7 - 5=2$ mm.

Answer:

$2$ mm