Question

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1. a triangle with sides measuring 3, 8, and 6 inches is dilated to create a triangle with sides measuring 10.5, 28, and 21 inches

Explanation:

Step1: Find the scale - factor

The original triangle has side - lengths 3, 8, and 6 inches. The dilated triangle has side - lengths 10.5, 28, and 21 inches. To find the scale - factor, we can divide the corresponding sides of the dilated triangle by the original triangle. Let's use the first pair of corresponding sides. The scale - factor $k=\frac{10.5}{3}=3.5$. We can check with the other sides: $\frac{28}{8} = 3.5$ and $\frac{21}{6}=3.5$.

Answer:

The scale - factor of the dilation is 3.5.