Question

Select One

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. Therefore, the segments RV and TV are equal in length because they are opposite segments formed by the diagonals.

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

Setting the two segments equal to each other:

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

To solve for \( y \), first reorganize the equation:

\[
18 + 10 = 3y - y
\]
\[
28 = 2y
\]

Now divide both sides by 2:

\[
y = 14
\]

Now we can find the lengths of RV and TV by substituting \( y \) back into the original expressions:

\[
RV = y + 18 = 14 + 18 = 32 \text{ units}
\]
\[
TV = 3y - 10 = 3(14) - 10 = 42 - 10 = 32 \text{ units}
\]

Since both \( RV \) and \( TV \) are equal, we find that diagonal \( RT \) is equal to the lengths of these segments. Therefore, diagonal RT is:

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

The answer is 64.