Question

if vw = wx = 74, vy = t + 46, and xy = 3t, what is xy? xy = \boxed{}

Explanation:

Step1: Apply the perpendicular bisector theorem

Since \(VW = WX = 74\) and \(WY\) is perpendicular to \(XV\), by the perpendicular bisector theorem, \(VY=XY\).

Step2: Set up the equation

Given \(VY=t + 46\) and \(XY = 3t\), we set \(t + 46=3t\).
Subtract \(t\) from both sides: \(46=3t - t\), so \(46 = 2t\).
Divide both sides by \(2\): \(t=\frac{46}{2}=23\).

Step3: Find \(XY\)

Substitute \(t = 23\) into \(XY = 3t\), then \(XY=3\times23 = 69\).

Answer:

\(69\)