Question

1. the two figures are similar. solve for the variables (x, y, and z) and give the scale factor of the small figure to the big figure.

Explanation:

Step1: Find the scale factor

Since the two figures are similar, the scale factor \(k\) of the small figure to the big figure is \(\frac{12}{28}=\frac{3}{7}\)

Step2: Solve for \(x\)

Using the proportion \(\frac{9}{x}=\frac{3}{7}\) (corresponding sides). Cross - multiply: \(3x = 9\times7\), so \(x=\frac{9\times7}{3}=21\)

Step3: Solve for \(y\)

Using the proportion \(\frac{y}{42}=\frac{3}{7}\) (corresponding sides). Cross - multiply: \(7y=42\times3\), so \(y = 18\)

Step4: Solve for \(z\)

Using the proportion \(\frac{z}{14}=\frac{3}{7}\) (corresponding sides). Cross - multiply: \(7z=14\times3\), so \(z = 6\)

Answer:

\(x = 21\), \(y = 18\), \(z = 6\), scale factor \(\frac{3}{7}\)