Question

what scale factor should you use? 64in 32in to scale back to the original, use a scale factor of

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ to go from a new size to the original size is the ratio of the original size to the new size. If we assume the rectangle has been scaled up and we want to go back to the original, and we can use either the length or the width. Let's use the length. Suppose the original length is $l_1$ and the new length is $l_2$. The scale - factor $k=\frac{l_1}{l_2}$.

Step2: Identify original and new lengths

Assume the original length is $x$ and the new length $l_2 = 64$ inches. If we assume the rectangle was scaled up from an original state, and we want to scale back, we consider the fact that the scale - factor is the reciprocal of the factor by which it was scaled up. Since we want to return to the original, if we assume the original length was half of the new length (a common scaling situation), the scale factor $k=\frac{1}{2}$ because if we multiply the new length by $\frac{1}{2}$, we get back to the original length. Mathematically, if we assume the original length $l_1$ and new length $l_2$, and we know that to reverse a scaling operation, the scale factor $k$ such that $l_1=k\times l_2$. If we take the ratio of the original size to the new size for the length (or width), for example, if the original width was $16$ and new width is $32$, or original length was $32$ and new length is $64$, the scale factor $k = \frac{1}{2}$.

Answer:

$\frac{1}{2}$