Question

if rs = 6x and ru = 8x - 18, find ru in parallelogram stuv. ru =

Explanation:

Step1: Set equal diagonals segments

In a parallelogram, diagonals bisect each other, so $RS = RU$.
$$6x = 8x - 18$$

Step2: Solve for $x$

Isolate $x$ by subtracting $6x$ and adding 18 to both sides.
$$18 = 8x - 6x \implies 18 = 2x \implies x = 9$$

Step3: Calculate $RU$

Substitute $x=9$ into $RU=8x-18$.
$$RU = 8(9) - 18 = 72 - 18$$

Answer:

54