Question

what is the scale factor from the original figure to the scaled copy? what is the length of the base in the scaled copy? units

Explanation:

Step1: Find the scale - factor

The scale - factor is found by comparing the corresponding heights of the original and scaled - copy triangles. The height of the original triangle is 12 and the height of the scaled - copy triangle is 36. The scale - factor $k$ is given by the ratio of the height of the scaled - copy to the height of the original, so $k=\frac{36}{12}=3$.

Step2: Find the base of the scaled - copy

Since the scale - factor is 3 and the base of the original triangle is 10, to find the base of the scaled - copy, we multiply the base of the original by the scale - factor. Let the base of the original be $b_1 = 10$ and the scale - factor be $k = 3$. Then the base of the scaled - copy $b_2=k\times b_1=3\times10 = 30$.

Answer:

30