Question

quadrilateral vwxy is a rhombus. what is xy?
vwxy is a rhombus figure, with side wx labeled 11x + 13 and side xy labeled 9x + 15.
xy =
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Explanation:

Step1: Recall rhombus side property

In a rhombus, all sides are equal. So, \(WX = XY\). Given \(WX = 11x + 13\) and \(XY = 9x + 15\), we set them equal: \(11x + 13 = 9x + 15\).

Step2: Solve for \(x\)

Subtract \(9x\) from both sides: \(11x - 9x + 13 = 9x - 9x + 15\), which simplifies to \(2x + 13 = 15\). Then subtract 13 from both sides: \(2x + 13 - 13 = 15 - 13\), so \(2x = 2\). Divide both sides by 2: \(x = 1\).

Step3: Find \(XY\)

Substitute \(x = 1\) into \(XY = 9x + 15\): \(XY = 9(1) + 15 = 9 + 15 = 24\).

Answer:

24