In a parallelogram, the diagonals bisect each other, which means that the lengths of the segments created by the diagonals are equal.
Given that \( RV \) measures \( y + 18 \) units and \( TV \) measures \( 3y - 10 \) units, we set these equal because diagonal \( RT \) is equal to the sum of both segments:
\[ y + 18 = 3y - 10 \]
Now, we'll solve for \( y \):
Subtract \( y \) from both sides:
\[ 18 = 2y - 10 \]
Add 10 to both sides:
\[ 28 = 2y \]
Divide by 2:
\[ y = 14 \]
Now that we have \( y \), we can find the lengths of \( RV \) and \( TV \):
Substituting \( y = 14 \) into \( RV \):
\[ RV = 14 + 18 = 32 \text{ units} \]
Substituting \( y = 14 \) into \( TV \):
\[ TV = 3(14) - 10 = 42 - 10 = 32 \text{ units} \]
Since both segments \( RV \) and \( TV \) are equal (as expected in a parallelogram), the length of diagonal \( RT \) is:
\[ RT = RV + TV = 32 + 32 = 64 \text{ units} \]
Therefore, the length of diagonal \( RT \) is 64 units.
The correct response is:
64