Question

in parallelogram rstu. rv measures y + 18 units and tv measures 3y - 10 units. how many units long is diagon rt?

Explanation:

Step1: Use property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So, \(RV = TV\).

$$y + 18=3y - 10$$

Step2: Solve for \(y\)

Subtract \(y\) from both sides:

$$18 = 2y-10$$

Add \(10\) to both sides:

$$28 = 2y$$

Divide both sides by \(2\):

$$y = 14$$

Step3: Find length of \(RT\)

Since \(RT=RV + TV\) and \(RV = TV\) (from parallelogram property), \(RT = 2RV\) (or \(2TV\)).
Substitute \(y = 14\) into \(RV=y + 18\): \(RV=14 + 18=32\).
Then \(RT = 2\times32=64\).

Answer:

\(64\)