Question
Use the image to answer the question.In parallelogram RSTU , RV measures y+18 units and TV measures 3y−10 units. How many units long is diagonal RT ?(1 point)Responses16166464141432
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GPT-4o mini
In a parallelogram, the diagonals bisect each other. Therefore, segments RV and TV must be equal in length.
Given:
- \( RV = y + 18 \)
- \( TV = 3y - 10 \)
Since they are equal, we set up the equation:
\[
y + 18 = 3y - 10
\]
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, we can find the lengths of \( RV \) and \( TV \):
- Find \( RV \):
\[
RV = y + 18 = 14 + 18 = 32
\]
- Find \( TV \):
\[
TV = 3y - 10 = 3(14) - 10 = 42 - 10 = 32
\]
Both \( RV \) and \( TV \) measure 32 units.
Since RT is a diagonal, and in a parallelogram the diagonals are equal in length, we conclude:
**Diagonal RT is 32 units long.**
The options do not list 32, so there may be a re-evaluation of the question. Please check to ensure no calculations or details were overlooked.
Given:
- \( RV = y + 18 \)
- \( TV = 3y - 10 \)
Since they are equal, we set up the equation:
\[
y + 18 = 3y - 10
\]
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, we can find the lengths of \( RV \) and \( TV \):
- Find \( RV \):
\[
RV = y + 18 = 14 + 18 = 32
\]
- Find \( TV \):
\[
TV = 3y - 10 = 3(14) - 10 = 42 - 10 = 32
\]
Both \( RV \) and \( TV \) measure 32 units.
Since RT is a diagonal, and in a parallelogram the diagonals are equal in length, we conclude:
**Diagonal RT is 32 units long.**
The options do not list 32, so there may be a re-evaluation of the question. Please check to ensure no calculations or details were overlooked.
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