Use the image to answer the question.

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

14
14

64
64

32
32

16
16

Answer 1

To find the length of diagonal RT in parallelogram RSTU, we can use the information given about the segments RV and TV, which are parts of the diagonal RT.

According to the problem:

• RV = y + 18
• TV = 3y - 10

Since V is the midpoint of diagonal RT, the two segments RV and TV are equal in length. Therefore, we set them equal to each other:

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

Now, we can solve for y:

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

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

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

Now that we have the value for y, we can find the lengths of segments RV and TV:

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

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

Both segments are the same length, confirming our calculations are consistent.

Thus, the total length of diagonal RT (which is the sum of the lengths of RV and TV) is: \[ RT = RV + TV = 32 + 32 = 64 \]

Therefore, the diagonal RT measures 64 units long.

The correct response is: 64