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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. 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.