Question

if vw = vy = 38, wx = 5s - 90, and xy = 2s, what is wx?

Explanation:

Step1: Apply the property of congruent - right - triangles

Since \(VW = VY\) and \(\angle WVX=\angle YVX = 90^{\circ}\) and \(VX\) is common to both \(\triangle WVX\) and \(\triangle YVX\), by the Hypotenuse - Leg (HL) congruence criterion for right - triangles, \(\triangle WVX\cong\triangle YVX\). So, \(WX = XY\).

Step2: Set up the equation

Set \(WX = XY\), so \(5s-90 = 2s\).

Step3: Solve the equation for \(s\)

Subtract \(2s\) from both sides: \(5s - 2s-90=2s - 2s\), which simplifies to \(3s-90 = 0\). Then add 90 to both sides: \(3s-90 + 90=0 + 90\), getting \(3s=90\). Divide both sides by 3: \(s=\frac{90}{3}=30\).

Step4: Find the length of \(WX\)

Substitute \(s = 30\) into the expression for \(WX\). \(WX=5s - 90\), so \(WX=5\times30-90\). First, calculate \(5\times30 = 150\), then \(150-90 = 60\).

Answer:

60