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: Use the property of congruent segments

Since \( QT = QS \) (by the property of the figure, likely a kite - two pairs of adjacent sides are equal), we set \( 6x - 3=3x + 4 \).

$$6x-3x=4 + 3$$

$$3x=7$$

$$x = 7$$

Step2: Find the length of \( RV \)

Substitute \( x = 7 \) into \( 2x+5 \).

$$2x+5=2\times7 + 5=14 + 5=19$$

Step3: Calculate the length of \( TV \)

Since \( TV = 2RV \) (because \( R \) is the mid - point of \( TV \), as the diagonals of a kite are perpendicular and one diagonal is bisected), \( TV=2\times19 = 38\) units.

Answer:

C. 38 units