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 16 16 64 64 14 14 Skip to navigation

Answer 1

In parallelogram RSTU, we know that the two opposite sides, RV and TV, are equal in length. This means:

$RV=TV$

Given:

• $RV=y+18$
• $TV=3y-10$

Setting the two expressions 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 by 2:

$$y=14$$

Now that we have the value of $y$, we can find the lengths of $RV$ and $TV$.

Substituting $y=14$ back into the expressions:

$$RV=y+18=14+18=32,\text{units}$$

$$TV=3y-10=3(14)-10=42-10=32,\text{units}$$

Both side lengths are indeed equal.

In a parallelogram, diagonal RT can be found using the lengths of the sides, but in this case, we can summarize that diagonal RT is a transversal connecting points R and T, and the measurements we've calculated apply to the triangle formed by these vertices.

Since the provided answer choices seem to suggest specific lengths for diagonal RT, and since RV = 32 units directly gives us insight into half of the diagonal triangle configuration, we will conclude:

For the choices provided, if we are only considering the lengths derived from segments RV and TV, the best logical assessment would yield RT as being effectively equal to one of the lengths derived.

Hence, the approximate length for diagonal RT in parallelogram RSTU is 32 units (Option 32).