In a parallelogram, the diagonals bisect each other. Therefore, the segments RV and TV are equal in length because they are opposite segments formed by the diagonals.
Given:
- \( RV = y + 18 \)
- \( TV = 3y - 10 \)
Setting the two segments equal to each other:
\[ y + 18 = 3y - 10 \]
To solve for \( y \), first reorganize the equation:
\[ 18 + 10 = 3y - y \] \[ 28 = 2y \]
Now divide both sides by 2:
\[ y = 14 \]
Now we can find the lengths of RV and TV by substituting \( y \) back into the original expressions:
\[ RV = y + 18 = 14 + 18 = 32 \text{ units} \] \[ TV = 3y - 10 = 3(14) - 10 = 42 - 10 = 32 \text{ units} \]
Since both \( RV \) and \( TV \) are equal, we find that diagonal \( RT \) is equal to the lengths of these segments. Therefore, diagonal RT is:
\[ RT = RV + TV = 32 + 32 = 64 \text{ units.} \]
The answer is 64.
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