To solve for the length of VT in the rhombus TURS where \( RV = 2x + 4 \) and \( VT = 8x - 8 \), we need to leverage the properties of the rhombus. In a rhombus, the diagonals bisect each other, which means that \( RV \) and \( VT \) must be equal in length at the point of intersection.
Step 1: Set up the equation.
Since \( RV = VT \), we can set the two expressions equal to each other: \[ 2x + 4 = 8x - 8 \]
Step 2: Solve for \( x \).
To isolate \( x \), we'll first subtract \( 2x \) from both sides: \[ 4 = 6x - 8 \]
Next, add \( 8 \) to both sides: \[ 12 = 6x \]
Now, divide both sides by \( 6 \): \[ x = 2 \]
Step 3: Substitute \( x \) back into the equation for VT.
Now that we have \( x \), we can find the length of \( VT \) by substituting \( x = 2 \) back into the expression for \( VT \): \[ VT = 8x - 8 \] \[ VT = 8(2) - 8 \] \[ VT = 16 - 8 \] \[ VT = 8 \]
Final Answer:
The length of \( VT \) is \( 8 \).