Determine if the triangles are similar. If so, state the reason. 8, 10, 15 24, 16, 12.8

Answer 1

To determine if the two triangles with sides 8, 10, and 15, and 24, 16, and 12.8 are similar, we can use the concept of side ratios.

First, we list the sides of each triangle:

• Triangle 1: 8, 10, 15
• Triangle 2: 24, 16, 12.8

Now, we will find the ratios of the corresponding sides of the triangles:

1. For side 8 (Triangle 1) and 24 (Triangle 2): \[ \frac{8}{24} = \frac{1}{3} \]

2. For side 10 (Triangle 1) and 16 (Triangle 2): \[ \frac{10}{16} = \frac{5}{8} \]

3. For side 15 (Triangle 1) and 12.8 (Triangle 2): \[ \frac{15}{12.8} = \frac{15}{12.8} = \frac{75}{64} \text{ (simplified)} \]

Now we compare the ratios:

• The ratio \(\frac{1}{3}\) does not match the other two ratios \(\frac{5}{8}\) and \(\frac{75}{64}\).

Since the ratios of the corresponding sides are not the same, the two triangles are not similar.

The conclusion is: The triangles are not similar because the ratios of their corresponding sides are not equal.