Parallelogram upper R upper S upper T upper U is shown with base upper T upper U larger than height upper S upper T. Diagonals are drawn from upper R to upper T and upper S to upper U to meet at upper V.

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

64
64

16
16

32

Answer 1

In a parallelogram, the diagonals bisect each other. This means that the lengths of the segments created by the intersection of the diagonals are equal.

Given that \( RV = y + 18 \) and \( TV = 3y - 10 \), we can set these equal to one another since \( RV = VT \):

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

To solve for \( y \), we can rearrange the equation:

\[ 18 + 10 = 3y - y \] \[ 28 = 2y \] \[ y = 14 \]

Now, we can find the lengths of \( RV \) and \( TV \):

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

Since the diagonals bisect each other, we have:

\[ RT = RV + VT = RV + RV = 2RV = 2(32) = 64 \quad \text{units} \]

Thus, the length of diagonal \( RT \) is:

\[ \boxed{64} \quad \text{units} \]