To find the lengths of the other two sides of the similar triangle, we can use the concept of similarity ratios.
First, we determine the ratio of the smallest side of the triangles. The smallest side of the first triangle is 4.2 inches, and the smallest side of the similar triangle is 1.4 inches.
The ratio is:
\[ \text{Ratio} = \frac{\text{Smallest side of similar triangle}}{\text{Smallest side of original triangle}} = \frac{1.4}{4.2} \]
Calculating this ratio:
\[ \frac{1.4}{4.2} = \frac{1.4 \div 1.4}{4.2 \div 1.4} = \frac{1}{3} \]
Now, we multiply the lengths of the other two sides of the original triangle by this ratio to find the corresponding sides of the similar triangle.
The sides of the original triangle are 5.7 inches and 7.2 inches.
- For the side of length 5.7 inches:
\[ \text{Length in similar triangle} = 5.7 \times \frac{1}{3} = \frac{5.7}{3} = 1.9 \text{ inches} \]
- For the side of length 7.2 inches:
\[ \text{Length in similar triangle} = 7.2 \times \frac{1}{3} = \frac{7.2}{3} = 2.4 \text{ inches} \]
Thus, the lengths of the other two sides of the similar triangle are:
- The smaller side length is 1.9 inches.
- The larger side length is 2.4 inches.
So, the final answer is:
The smaller side length is 1.9 inches and the larger side length is 2.4 inches.