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) 14 16 64 32

Explanation:

Step1: Use property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So $RV = TV$. Set up the equation $y + 18=3y - 10$.

Step2: 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 $y = 14$.

Step3: Find length of $RV$

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

Step4: Find length of $RT$

Since $RT=2RV$ (because diagonals bisect each other), $RT = 2\times32=64$.

Answer:

C. 64