Question

3
triangle a has sides 10, 15, 18 and some angles marked. triangle b has sides 6, 4, 7.2 and some angles marked. the triangles seem to be related, likely for a similarity or ratio problem.

Explanation:

To determine if triangles \( A \) and \( B \) are similar, we check the ratios of their corresponding sides.

Step 1: Identify corresponding sides

• For triangle \( A \): sides are \( 10 \), \( 15 \), \( 18 \)
• For triangle \( B \): sides are \( 4 \), \( 6 \), \( 7.2 \)

Step 2: Calculate the ratios of corresponding sides

• Ratio of \( 10 \) (A) to \( 4 \) (B): \( \frac{10}{4} = 2.5 \)
• Ratio of \( 15 \) (A) to \( 6 \) (B): \( \frac{15}{6} = 2.5 \)
• Ratio of \( 18 \) (A) to \( 7.2 \) (B): \( \frac{18}{7.2} = 2.5 \)

Since all three ratios are equal (\( 2.5 \)), the triangles are similar by the Side - Side - Side (SSS) similarity criterion.

If we wanted to find a missing side (though in this case all sides are given for the check), we would set up a proportion using the known ratio. For example, if a side \( x \) in triangle \( A \) corresponds to a side \( y \) in triangle \( B \), then \( \frac{x}{y}=2.5 \), so \( x = 2.5y \) or \( y=\frac{x}{2.5} \)

Answer:

The triangles are similar with a scale factor of \( 2.5 \) (or \( \frac{5}{2} \))