In parallelogram RSTU, diagonals bisect each other. Therefore, diagonal RT can be calculated by adding segments RV and TV.
Given:
- \( RV = y + 18 \)
- \( TV = 3y - 10 \)
To find the length of diagonal RT, we need to find the value of \( y \). Since RV and TV are equal in length (as they are opposite segments formed by the diagonals), we set them equal:
\[ y + 18 = 3y - 10 \]
Now, solve for \( y \):
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Subtract \( y \) from both sides: \[ 18 = 2y - 10 \]
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Add 10 to both sides: \[ 28 = 2y \]
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Divide by 2: \[ y = 14 \]
Now substitute \( y = 14 \) back into the expressions for RV and TV:
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Calculate \( RV \): \[ RV = 14 + 18 = 32 \]
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Calculate \( TV \): \[ TV = 3(14) - 10 = 42 - 10 = 32 \]
Both segments are equal, confirming that: \[ RT = RV + TV = 32 + 32 = 64 \]
Thus, the length of diagonal RT is 64 units.
The answer is 64.
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