in the diagram, the length of segment tr can be represented by 5x - 4. what is the length of segment vs? 3…

Explanation:

Step1: Use property of rhombus diagonals

In a rhombus, the diagonals are perpendicular bisectors of each other. So, $TR = VR$. Set up the equation $5x - 4=3x + 4$.

Step2: Solve the equation for x

Subtract $3x$ from both sides: $5x-3x - 4=3x-3x + 4$, which simplifies to $2x-4 = 4$. Then add 4 to both sides: $2x-4 + 4=4 + 4$, giving $2x=8$. Divide both sides by 2: $x = 4$.

Step3: Find the length of VS

Since $VS=2x + 5$, substitute $x = 4$ into the expression. So, $VS=2\times4+5=8 + 5=13$.

Answer:

13 units