Use the image to answer the question.In parallelogram  RSTU ,  RV  measures  y+18  units and  TV  measures  3y−10  units. How many units long is diagonal  RT ?(1 point)Responses16166464141432

1 answer

In a parallelogram, the diagonals bisect each other. Therefore, segments RV and TV must be equal in length.

Given:

  • \( RV = y + 18 \)
  • \( TV = 3y - 10 \)

Since they are equal, we set up the equation:

\[ y + 18 = 3y - 10 \]

Now, solve for \( y \):

  1. Subtract \( y \) from both sides:

\[ 18 = 2y - 10 \]

  1. Add 10 to both sides:

\[ 28 = 2y \]

  1. Divide by 2:

\[ y = 14 \]

Now, we can find the lengths of \( RV \) and \( TV \):

  • Find \( RV \):

\[ RV = y + 18 = 14 + 18 = 32 \]

  • Find \( TV \):

\[ TV = 3y - 10 = 3(14) - 10 = 42 - 10 = 32 \]

Both \( RV \) and \( TV \) measure 32 units.

Since RT is a diagonal, and in a parallelogram the diagonals are equal in length, we conclude:

Diagonal RT is 32 units long.

The options do not list 32, so there may be a re-evaluation of the question. Please check to ensure no calculations or details were overlooked.

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