Questions: Are the triangles similar?

Solution Steps

Identify the corresponding sides of the two triangles. The sides of the first triangle are 10, 16, and 20. The sides of the second triangle are 2, 3, and 4.

Calculate the ratios of the corresponding sides:

• Ratio of the smallest sides: \( \frac{10}{2} = 5 \)
• Ratio of the middle sides: \( \frac{16}{3} \approx 5.33 \)
• Ratio of the largest sides: \( \frac{20}{4} = 5 \)

Compare the ratios of the corresponding sides. For the triangles to be similar, all corresponding side ratios must be equal. Here, the ratios are 5, 5.33, and 5, which are not equal.

Final Answer