in the diagram, the length of segment vs is 39 units. what is the length of segment tv? 14 units 19 units 38…

Explanation:

Step1: Set up equation for VS

Since $VS=(3x + 4)+(2x + 5)$ and $VS = 39$, we have $(3x + 4)+(2x + 5)=39$. Combining like - terms: $3x+2x+4 + 5=39$, which simplifies to $5x+9 = 39$.

Step2: Solve for x

Subtract 9 from both sides of the equation: $5x+9−9=39−9$, so $5x=30$. Divide both sides by 5: $\frac{5x}{5}=\frac{30}{5}$, then $x = 6$.

Step3: Find length of TV

Since $TV = 2(2x + 5)$ (because the diagonals of a rhombus bisect each other), substitute $x = 6$ into $2x+5$. First, find the value of $2x + 5$ when $x = 6$: $2\times6+5=12 + 5=17$. Then $TV=2\times17 = 34$. But there is a mistake above. Since the diagonals of a rhombus are perpendicular bisectors of each other, we know that $3x + 4=2x+5$ (because the two segments on diagonal $QS$ are equal in a rhombus). Solve $3x + 4=2x+5$ for $x$: $3x-2x=5 - 4$, so $x = 1$. The length of $TV$: Since $TV = 2(2x + 5)$, substitute $x = 1$ into it. $2x+5=2\times1+5=7$, and $TV = 2\times19=38$ (because $TV$ is composed of two equal segments of length $2x + 5$).

Answer:

38 units