Question

quadrilateral rstu is a parallelogram. what must be the value of x? 2 4 5 10

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So, \( UV = VS \).
Given \( UV=(x - 3)\text{ m}\) and \( VS=(3x - 13)\text{ m}\), we set up the equation \( x-3=3x - 13\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides:
\(x-3-x=3x - 13-x\)
\(- 3=2x-13\)
Add \(13\) to both sides:
\(-3 + 13=2x-13 + 13\)
\(10=2x\)
Divide both sides by \(2\):
\(x=\frac{10}{2}\)

Answer:

\(5\) (corresponding to the third option)