Question

question 5 (multiple choice worth 1 points) (02.06r mc) the diagonals of parallelogram qrst intersect at point u. if tu = 3x + 10 and ru = 5x - 4, what is ru? 2 7 22 31

Explanation:

Step1: Use property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So \(TU = RU\).
$$3x + 10=5x - 4$$

Step2: Solve for \(x\)

Subtract \(3x\) from both sides:
$$10 = 2x-4$$
Add \(4\) to both sides:
$$14 = 2x$$
Divide both sides by \(2\):
$$x = 7$$

Step3: Find \(RU\)

Substitute \(x = 7\) into \(RU=5x - 4\):
$$RU=5\times7 - 4=35 - 4=31$$

Answer:

31