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 14 14 32 32 64 64 16

Answer 1

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**.