In parallelogram RSTU , RV measures y+18 units and TV measures 3y−10 units. How many units long is diagonal RT ? (1 point) Responses 14 14 32 32 64 64 16

1 answer

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 \( y \):

  1. Subtract \( y \) from both sides: \[ 18 = 2y - 10 \]

  2. Add 10 to both sides: \[ 28 = 2y \]

  3. Divide by 2: \[ y = 14 \]

Now substitute \( y = 14 \) back into the expressions for RV and TV:

  1. Calculate \( RV \): \[ RV = 14 + 18 = 32 \]

  2. 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.