Let the sides of the first triangle be denoted as \( a = 4.2 \), \( b = 5.7 \), and \( c = 7.2 \) inches. The smallest side of the triangle is \( a = 4.2 \) inches.
The sides of a similar triangle are proportional to the sides of the first triangle. Given that the smallest side of the similar triangle is \( 1.4 \) inches, we can set up the ratio of the sides:
\[ \frac{1.4}{4.2} = \frac{x}{a} \]
To find the ratio, we calculate:
\[ \frac{1.4}{4.2} = \frac{1.4 \div 1.4}{4.2 \div 1.4} = \frac{1}{3} \]
This means the sides of the similar triangle are \( \frac{1}{3} \) of the lengths of the corresponding sides of the first triangle.
Now we can find the lengths of the other two sides of the similar triangle:
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For side \( b \): \[ b' = b \times \frac{1}{3} = 5.7 \times \frac{1}{3} = 1.9 \text{ inches} \]
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For side \( c \): \[ c' = c \times \frac{1}{3} = 7.2 \times \frac{1}{3} = 2.4 \text{ inches} \]
Thus, the lengths of the other two sides of the similar triangle are:
\[ \text{First side} = 1.9 \text{ inches}, \quad \text{Second side} = 2.4 \text{ inches} \]
In summary, the lengths of the corresponding sides in the similar triangle are:
- 1.4 inches (smallest side)
- 1.9 inches (medium side)
- 2.4 inches (largest side)