Question

1. using the digits 0 to 9 without repetition, fill in the blanks to make rectangles that are scaled copies.

Explanation:

Step1: Recall property of scaled - copies

Scaled copies have equal ratios of corresponding side - lengths. For rectangles, if the side - lengths of one rectangle are \(a\) and \(b\), and of another are \(c\) and \(d\), then \(\frac{a}{b}=\frac{c}{d}\).

Step2: Try digit combinations

We know that ratios like \(1:2\), \(2:4\), \(3:6\), \(4:8\) are equivalent. Let's assume the first rectangle has side - lengths \(1\) and \(2\). The second rectangle could have side - lengths \(3\) and \(6\).
One possible solution: For the first rectangle, the side - lengths can be \(1\) and \(2\) (smaller rectangle). For the second rectangle, the side - lengths can be \(3\) and \(6\).

Answer:

First rectangle: 1, 2; Second rectangle: 3, 6 (There are other possible combinations such as 2, 4 and 5, 10 etc. as long as the ratio of side - lengths is the same and digits are not repeated)