Question

in the diagram, the length of segment vs is 39 units. what is the length of segment tv? 14 units 19 units 38 units 50 units

Explanation:

Step1: Set up equation for VS

Since $VS=(3x + 4)+(2x+5)$ and $VS = 39$, we have $(3x + 4)+(2x+5)=39$.

Step2: Simplify left - hand side

Combine like terms: $3x+2x+4 + 5=39$, which gives $5x+9 = 39$.

Step3: Solve for x

Subtract 9 from both sides: $5x=39 - 9=30$. Then divide by 5, so $x=\frac{30}{5}=6$.

Step4: Find length of TV

$TV = 2(2x + 5)$. Substitute $x = 6$ into the expression: $2x+5=2\times6 + 5=12 + 5 = 17$. Then $TV=2\times17=38$ units.

Answer:

C. 38 units