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Question

Parallelogram upper R upper S upper T upper U is shown with base upper T upper U larger than height upper S upper T. Diagonals are drawn from upper R to upper T and upper S to upper U to meet at upper V.

In parallelogram RSTU
, RV
measures y+18
units and TV
measures 3y−10
units. How many units long is diagonal RT
?

(1 point)
Responses

16
16

14
14

64
64

32
32
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Answer 1

In parallelogram RSTU, the diagonals bisect each other. Therefore, we have:

\[ RV = TV \]

From the problem, we have the following expressions for the lengths of the segments:

1. \( RV = y + 18 \)
2. \( TV = 3y - 10 \)

Setting these two expressions equal gives us:

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

Now, we can solve for \( y \):

1. Rearranging the equation:

   \( 18 + 10 = 3y - y \)

   \( 28 = 2y \)

2. Dividing both sides by 2:

   \( y = 14 \)

Now we can substitute \( y \) back into the expressions for \( RV \) or \( TV \) to find the length of one of the segments:

Calculating \( RV \):

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

Calculating \( TV \):

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

Since both \( RV \) and \( TV \) are equal and each measures \( 32 \) units, we can find the length of diagonal \( RT \) by adding these two segments:

\[ RT = RV + TV = 32 + 32 = 64 \]

Thus, the length of diagonal \( RT \) is

64 units.