To find the lengths of the other two sides of the similar triangle, we can use the property of similar triangles which states that the ratios of corresponding side lengths are equal.
First, we determine the scale factor between the triangles. The smallest side of the original triangle is 4.2, and the smallest side of the similar triangle is 1.4.
The scale factor (k) can be calculated as follows:
\[ k = \frac{\text{smallest side of similar triangle}}{\text{smallest side of original triangle}} = \frac{1.4}{4.2} \]
Calculating this gives:
\[ k = \frac{1.4}{4.2} = \frac{1.4 \div 1.4}{4.2 \div 1.4} = \frac{1}{3} \]
Now, we can find the lengths of the other two sides in the similar triangle by multiplying the lengths of the sides of the original triangle by the scale factor \( k \).
The other two sides of the original triangle are 5.7 and 7.2. We will calculate each:
- For the side length of 5.7:
\[ \text{New side} = 5.7 \times k = 5.7 \times \frac{1}{3} = \frac{5.7}{3} = 1.9 \]
- For the side length of 7.2:
\[ \text{New side} = 7.2 \times k = 7.2 \times \frac{1}{3} = \frac{7.2}{3} = 2.4 \]
Thus, the lengths of the other two sides of the similar triangle are 1.9 and 2.4.