Question

Question 17
A)
In the diagram below, quadrilateral TURS is a rhombus. If RV = 2x+4 and VT = 8x-8, find the length of VT. You must show all steps in order to receive full credit. You may upload a picture of your work by using the icon or your may type out your work.

Answer 1

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 \( 8 \).