Question

what is the scale factor from the original figure to the scaled copy? 3 what is the length of the base in the scaled copy? units

Explanation:

Step1: Find the scale factor

The scale factor is the ratio of the corresponding sides of the scaled - copy to the original. Given the corresponding heights \(h_1 = 12\) (original) and \(h_2=36\) (scaled - copy). The scale factor \(k=\frac{h_2}{h_1}\).

$$k = \frac{36}{12}=3$$

Step2: Find the base of the scaled - copy

Let the base of the original be \(b_1 = 10\) and the base of the scaled - copy be \(b_2\). Since the scale factor \(k = 3\) and \(k=\frac{b_2}{b_1}\), we can solve for \(b_2\).

$$b_2=k\times b_1$$

Substitute \(k = 3\) and \(b_1 = 10\) into the formula.

$$b_2=3\times10 = 30$$

Answer:

The scale factor is \(3\) and the length of the base in the scaled copy is \(30\) units.