Question

side length of original triangle, corresponding side length in scaled copy, 3, 9, 4, 12, the scale factor is

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ from the original figure to the scaled - copy is given by $k=\frac{\text{side length in scaled copy}}{\text{side length of original figure}}$.

Step2: Calculate scale factor using first pair

For the first pair of side lengths, where the side length of the original triangle is $a = 3$ and the corresponding side length in the scaled copy is $b = 9$. Using the formula $k=\frac{b}{a}$, we have $k=\frac{9}{3}=3$.

Step3: Verify with second pair

For the second pair, the side length of the original triangle is $a'=4$ and the corresponding side length in the scaled copy is $b' = 12$. Using the formula $k=\frac{b'}{a'}$, we get $k=\frac{12}{4}=3$.

Answer:

3