Question

calculate yz if wy = 23.8, xy = 22, and vz = 43
yz =

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle WVZ\sim\triangle WXY\), we have the proportion \(\frac{WY}{WZ}=\frac{XY}{VZ}\). Let \(YZ = x\), then \(WZ=WY + YZ=23.8+x\).

Step2: Substitute the values into the proportion

Substituting \(WY = 23.8\), \(XY = 22\), and \(VZ = 43\) into \(\frac{WY}{WZ}=\frac{XY}{VZ}\), we get \(\frac{23.8}{23.8 + x}=\frac{22}{43}\).

Step3: Cross - multiply

Cross - multiplying gives \(23.8\times43=22\times(23.8 + x)\).
First, calculate \(23.8\times43 = 1023.4\) and \(22\times23.8=523.6\). So the equation becomes \(1023.4=523.6+22x\).

Step4: Solve for \(x\)

Subtract \(523.6\) from both sides: \(1023.4 - 523.6=22x\), which gives \(499.8 = 22x\). Then \(x=\frac{499.8}{22}=22.7\).

Answer:

\(22.7\)