Question

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

(1 point)
Responses

32
32

14
14

16
16

64

Answer 1

In a parallelogram, the diagonals bisect each other, which means that the lengths of the segments created by the diagonals are equal.

Given that \( RV \) measures \( y + 18 \) units and \( TV \) measures \( 3y - 10 \) units, we set these equal because diagonal \( RT \) is equal to the sum of both segments:

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

Now, we'll solve for \( y \):

Subtract \( y \) from both sides:

\[
18 = 2y - 10
\]

Add 10 to both sides:

\[
28 = 2y
\]

Divide by 2:

\[
y = 14
\]

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

Substituting \( y = 14 \) into \( RV \):

\[
RV = 14 + 18 = 32 \text{ units}
\]

Substituting \( y = 14 \) into \( TV \):

\[
TV = 3(14) - 10 = 42 - 10 = 32 \text{ units}
\]

Since both segments \( RV \) and \( TV \) are equal (as expected in a parallelogram), the length of diagonal \( RT \) is:

\[
RT = RV + TV = 32 + 32 = 64 \text{ units}
\]

Therefore, the length of diagonal \( RT \) is **64 units**.

The correct response is:

**64**