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) 32 64 16 14

Explanation:

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. So, $RV = TV$.

Step2: Set up the equation

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

Step3: Solve for y

Subtract y from both sides: $18 = 2y-10$. Then add 10 to both sides: $28 = 2y$. Divide both sides by 2, we get $y = 14$.

Step4: Find length of RV

Substitute $y = 14$ into the expression for $RV$: $RV=y + 18=14 + 18=32$.

Step5: Find length of RT

Since $RT=RV + TV$ and $RV = TV$, then $RT = 2RV$. So $RT=2\times32 = 64$.

Answer:

64