Question

A triangle has sides of lengths 4.2, 5.7, and 7.2 inches. The smallest side of a similar triangle is 1.4 inches. What are the lengths of the other two sides? Write the smaller side length first and the larger side length second

Answer 1

To find the lengths of the other two sides of a similar triangle, we can use the property of similar triangles, which states that the ratios of the lengths of corresponding sides are equal.

Given the side lengths of the original triangle:
- \( a = 4.2 \) inches
- \( b = 5.7 \) inches
- \( c = 7.2 \) inches

The smallest side of the original triangle is \( 4.2 \) inches and the smallest side of the similar triangle is \( 1.4 \) inches.

First, find the scaling factor (ratio) between the small sides:
\[
\text{Scaling Factor} = \frac{1.4}{4.2}
\]

Calculating the scaling factor:
\[
\text{Scaling Factor} = \frac{1.4}{4.2} = \frac{1.4 \div 1.4}{4.2 \div 1.4} = \frac{1}{3} \approx 0.3333
\]

Now, we will apply this scaling factor to the other two sides \( 5.7 \) inches and \( 7.2 \) inches:

1. For side \( b = 5.7 \) inches:
\[
b' = 5.7 \times \frac{1}{3} = 1.9 \text{ inches}
\]

2. For side \( c = 7.2 \) inches:
\[
c' = 7.2 \times \frac{1}{3} = 2.4 \text{ inches}
\]

Thus, the lengths of the other two sides of the similar triangle are \( 1.9 \) inches and \( 2.4 \) inches. Writing the smaller side length first and the larger side length second, we have:

**1.9 inches, 2.4 inches.**