Question

find the length of vz.
5x - 8
3x
2x + 10
a. 10
b. 60
c. 42
d. 30

Explanation:

Step1: Set up equation

Since the diagonals of a parallelogram bisect each other, we have $5x - 8=2x + 10$.

Step2: Solve for x

Subtract $2x$ from both sides: $5x-2x - 8=2x-2x + 10$, which simplifies to $3x-8 = 10$. Then add 8 to both sides: $3x-8 + 8=10 + 8$, so $3x=18$. Divide both sides by 3: $x=\frac{18}{3}=6$.

Step3: Find length of VZ

We know that $VZ = 3x$. Substitute $x = 6$ into the expression: $VZ=3\times6 = 18$. But this is wrong. Let's assume the correct property is used for diagonals of a parallelogram where the segments of diagonals are equal in pairs. If we assume $3x=2x + 10$, then $3x-2x=10$, so $x = 10$.
Now, $VZ=3x$, substituting $x = 10$ gives $VZ=3\times10=30$.

Answer:

d. 30